diff --git a/ProcessLib/SmallDeformation/Tests.cmake b/ProcessLib/SmallDeformation/Tests.cmake
index 21cfc35b8d1045798c6bac8b418462e7f7692d84..57fcdd54a009f1ad990bb2917b52e0e36bec8efe 100644
--- a/ProcessLib/SmallDeformation/Tests.cmake
+++ b/ProcessLib/SmallDeformation/Tests.cmake
@@ -51,6 +51,7 @@ endif()
if (OGS_USE_MPI)
# OgsTest(WRAPPER mpirun -np 4 PROJECTFILE Mechanics/Linear/disc_with_hole.prj)
+ OgsTest(WRAPPER mpirun -np 2 PROJECTFILE Mechanics/InitialStates/soil_column_nonequilibrium_sigma_elementwise.prj)
endif()
if (OGS_USE_MFRONT)
diff --git a/Tests/Data/Mechanics/InitialStates/soil_column_bottom_partitioned_cell_properties_cfg2.bin b/Tests/Data/Mechanics/InitialStates/soil_column_bottom_partitioned_cell_properties_cfg2.bin
new file mode 100644
index 0000000000000000000000000000000000000000..25a56b8b2e51801712a3ef30c75f5458926d326a
Binary files /dev/null and b/Tests/Data/Mechanics/InitialStates/soil_column_bottom_partitioned_cell_properties_cfg2.bin differ
diff --git a/Tests/Data/Mechanics/InitialStates/soil_column_bottom_partitioned_cell_properties_val2.bin b/Tests/Data/Mechanics/InitialStates/soil_column_bottom_partitioned_cell_properties_val2.bin
new file mode 100644
index 0000000000000000000000000000000000000000..05a13f7ad50b5b90d969e11282aed55d2d053567
Binary files /dev/null and b/Tests/Data/Mechanics/InitialStates/soil_column_bottom_partitioned_cell_properties_val2.bin differ
diff --git a/Tests/Data/Mechanics/InitialStates/soil_column_bottom_partitioned_msh_cfg2.bin b/Tests/Data/Mechanics/InitialStates/soil_column_bottom_partitioned_msh_cfg2.bin
new file mode 100644
index 0000000000000000000000000000000000000000..9903ca1abe50deb4864cee34e170631c96618d2e
Binary files /dev/null and b/Tests/Data/Mechanics/InitialStates/soil_column_bottom_partitioned_msh_cfg2.bin differ
diff --git a/Tests/Data/Mechanics/InitialStates/soil_column_bottom_partitioned_msh_ele2.bin b/Tests/Data/Mechanics/InitialStates/soil_column_bottom_partitioned_msh_ele2.bin
new file mode 100644
index 0000000000000000000000000000000000000000..7d0392c3f5170652bdda7bdf7255b1f8af19a804
Binary files /dev/null and b/Tests/Data/Mechanics/InitialStates/soil_column_bottom_partitioned_msh_ele2.bin differ
diff --git a/Tests/Data/Mechanics/InitialStates/soil_column_bottom_partitioned_msh_ele_g2.bin b/Tests/Data/Mechanics/InitialStates/soil_column_bottom_partitioned_msh_ele_g2.bin
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/Tests/Data/Mechanics/InitialStates/soil_column_bottom_partitioned_msh_nod2.bin b/Tests/Data/Mechanics/InitialStates/soil_column_bottom_partitioned_msh_nod2.bin
new file mode 100644
index 0000000000000000000000000000000000000000..397dfc238d27388fca6619bd85df6f3316326b09
Binary files /dev/null and b/Tests/Data/Mechanics/InitialStates/soil_column_bottom_partitioned_msh_nod2.bin differ
diff --git a/Tests/Data/Mechanics/InitialStates/soil_column_bottom_partitioned_node_properties_cfg2.bin b/Tests/Data/Mechanics/InitialStates/soil_column_bottom_partitioned_node_properties_cfg2.bin
new file mode 100644
index 0000000000000000000000000000000000000000..02dba888ca799ac0ebd79efd5517f11823592525
Binary files /dev/null and b/Tests/Data/Mechanics/InitialStates/soil_column_bottom_partitioned_node_properties_cfg2.bin differ
diff --git a/Tests/Data/Mechanics/InitialStates/soil_column_bottom_partitioned_node_properties_val2.bin b/Tests/Data/Mechanics/InitialStates/soil_column_bottom_partitioned_node_properties_val2.bin
new file mode 100644
index 0000000000000000000000000000000000000000..e8a95df72230c122826eacfbcccf0f364eb4855e
Binary files /dev/null and b/Tests/Data/Mechanics/InitialStates/soil_column_bottom_partitioned_node_properties_val2.bin differ
diff --git a/Tests/Data/Mechanics/InitialStates/soil_column_left_partitioned_cell_properties_cfg2.bin b/Tests/Data/Mechanics/InitialStates/soil_column_left_partitioned_cell_properties_cfg2.bin
new file mode 100644
index 0000000000000000000000000000000000000000..fbe6218eccd824e69ecbc4dfd08f92dd5de0d139
Binary files /dev/null and b/Tests/Data/Mechanics/InitialStates/soil_column_left_partitioned_cell_properties_cfg2.bin differ
diff --git a/Tests/Data/Mechanics/InitialStates/soil_column_left_partitioned_cell_properties_val2.bin b/Tests/Data/Mechanics/InitialStates/soil_column_left_partitioned_cell_properties_val2.bin
new file mode 100644
index 0000000000000000000000000000000000000000..b1ab73110ec05ba7bb9374150b9e14aa5533b81d
Binary files /dev/null and b/Tests/Data/Mechanics/InitialStates/soil_column_left_partitioned_cell_properties_val2.bin differ
diff --git a/Tests/Data/Mechanics/InitialStates/soil_column_left_partitioned_msh_cfg2.bin b/Tests/Data/Mechanics/InitialStates/soil_column_left_partitioned_msh_cfg2.bin
new file mode 100644
index 0000000000000000000000000000000000000000..56d689bd170b1c603f3b7265a99a480827f4e74a
Binary files /dev/null and b/Tests/Data/Mechanics/InitialStates/soil_column_left_partitioned_msh_cfg2.bin differ
diff --git a/Tests/Data/Mechanics/InitialStates/soil_column_left_partitioned_msh_ele2.bin b/Tests/Data/Mechanics/InitialStates/soil_column_left_partitioned_msh_ele2.bin
new file mode 100644
index 0000000000000000000000000000000000000000..f680466d6335dfc9face022190804916181d461b
Binary files /dev/null and b/Tests/Data/Mechanics/InitialStates/soil_column_left_partitioned_msh_ele2.bin differ
diff --git a/Tests/Data/Mechanics/InitialStates/soil_column_left_partitioned_msh_ele_g2.bin b/Tests/Data/Mechanics/InitialStates/soil_column_left_partitioned_msh_ele_g2.bin
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/Tests/Data/Mechanics/InitialStates/soil_column_left_partitioned_msh_nod2.bin b/Tests/Data/Mechanics/InitialStates/soil_column_left_partitioned_msh_nod2.bin
new file mode 100644
index 0000000000000000000000000000000000000000..713af52b8468caab27878bd1dbc7f12c819d7e2d
Binary files /dev/null and b/Tests/Data/Mechanics/InitialStates/soil_column_left_partitioned_msh_nod2.bin differ
diff --git a/Tests/Data/Mechanics/InitialStates/soil_column_left_partitioned_node_properties_cfg2.bin b/Tests/Data/Mechanics/InitialStates/soil_column_left_partitioned_node_properties_cfg2.bin
new file mode 100644
index 0000000000000000000000000000000000000000..fa2afacbecea341917b930cb069307d0ee170821
Binary files /dev/null and b/Tests/Data/Mechanics/InitialStates/soil_column_left_partitioned_node_properties_cfg2.bin differ
diff --git a/Tests/Data/Mechanics/InitialStates/soil_column_left_partitioned_node_properties_val2.bin b/Tests/Data/Mechanics/InitialStates/soil_column_left_partitioned_node_properties_val2.bin
new file mode 100644
index 0000000000000000000000000000000000000000..56eda696176859e3739f45a76ee6da57069886c8
Binary files /dev/null and b/Tests/Data/Mechanics/InitialStates/soil_column_left_partitioned_node_properties_val2.bin differ
diff --git a/Tests/Data/Mechanics/InitialStates/soil_column_nonequilibrium_sigma_elementwise_ts_1.pvtu b/Tests/Data/Mechanics/InitialStates/soil_column_nonequilibrium_sigma_elementwise_ts_1.pvtu
new file mode 100644
index 0000000000000000000000000000000000000000..e2f1dfe2db6595d2b5980803a896931108dd9ba7
--- /dev/null
+++ b/Tests/Data/Mechanics/InitialStates/soil_column_nonequilibrium_sigma_elementwise_ts_1.pvtu
@@ -0,0 +1,43 @@
+<?xml version="1.0"?>
+<VTKFile type="PUnstructuredGrid" version="0.1" byte_order="LittleEndian" header_type="UInt32" compressor="vtkZLibDataCompressor">
+ <PUnstructuredGrid GhostLevel="1">
+ <FieldData>
+ <DataArray type="Int8" Name="IntegrationPointMetaData" NumberOfTuples="97" format="binary" RangeMin="34" RangeMax="125">
+ AQAAAACAAABhAAAAVgAAAA==eF5VjDEOgDAIAP/C7KZTv2IMQUXDADS0Dqbp3+3qeHfJNRCrfAdVccPsg5Ai6C2Q1vaLHicHpHkCI2VIUORWQskwzKM7B/qFh2t2Y6tjsPStfwt7JC0=
+ </DataArray>
+ <DataArray type="Int8" Name="OGS_VERSION" NumberOfTuples="40" format="binary" RangeMin="45" RangeMax="121">
+ AQAAAACAAAAoAAAAMAAAAA==eF4z0zPWM9Q1MtdNNzNOsTS3MEs110vJLCqp1DMyMDIwMDMyMDQxNTI0BwDHbAmw
+ </DataArray>
+ <DataArray type="Float64" Name="sigma_ip" NumberOfComponents="4" NumberOfTuples="198" format="binary" RangeMin="2184903.3215410206" RangeMax="3531311.24553486">
+ AQAAAACAAADAGAAAzgIAAA==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
+ <InformationKey name="L2_NORM_RANGE" location="vtkDataArray" length="2">
+ <Value index="0">
+ 2184903.3215
+ </Value>
+ <Value index="1">
+ 3531311.2455
+ </Value>
+ </InformationKey>
+ </DataArray>
+ </FieldData>
+ <PPointData>
+ <PDataArray type="Float64" Name="MaterialForces" NumberOfComponents="2"/>
+ <PDataArray type="Float64" Name="NodalForces" NumberOfComponents="2"/>
+ <PDataArray type="Float64" Name="displacement" NumberOfComponents="2"/>
+ <PDataArray type="Float64" Name="epsilon" NumberOfComponents="4"/>
+ <PDataArray type="Float64" Name="sigma" NumberOfComponents="4"/>
+ </PPointData>
+ <PCellData>
+ <PDataArray type="Float64" Name="nonequilibrium_stress" NumberOfComponents="4"/>
+ <PDataArray type="Float64" Name="principal_stress_values" NumberOfComponents="3"/>
+ <PDataArray type="Float64" Name="principal_stress_vector_1" NumberOfComponents="3"/>
+ <PDataArray type="Float64" Name="principal_stress_vector_2" NumberOfComponents="3"/>
+ <PDataArray type="Float64" Name="principal_stress_vector_3" NumberOfComponents="3"/>
+ </PCellData>
+ <PPoints>
+ <PDataArray type="Float64" Name="Points" NumberOfComponents="3"/>
+ </PPoints>
+ <Piece Source="soil_column_nonequilibrium_sigma_elementwise_ts_1_0.vtu"/>
+ <Piece Source="soil_column_nonequilibrium_sigma_elementwise_ts_1_1.vtu"/>
+ </PUnstructuredGrid>
+</VTKFile>
diff --git a/Tests/Data/Mechanics/InitialStates/soil_column_nonequilibrium_sigma_elementwise_ts_1_0.vtu b/Tests/Data/Mechanics/InitialStates/soil_column_nonequilibrium_sigma_elementwise_ts_1_0.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..d647911fc780ec5c073d014c31fb9f5cd0d0058f
--- /dev/null
+++ b/Tests/Data/Mechanics/InitialStates/soil_column_nonequilibrium_sigma_elementwise_ts_1_0.vtu
@@ -0,0 +1,37 @@
+<?xml version="1.0"?>
+<VTKFile type="UnstructuredGrid" version="0.1" byte_order="LittleEndian" header_type="UInt32" compressor="vtkZLibDataCompressor">
+ <UnstructuredGrid>
+ <FieldData>
+ <DataArray type="Int8" Name="IntegrationPointMetaData" NumberOfTuples="97" format="appended" RangeMin="34" RangeMax="125" offset="0" />
+ <DataArray type="Int8" Name="OGS_VERSION" NumberOfTuples="40" format="appended" RangeMin="45" RangeMax="121" offset="140" />
+ <DataArray type="Float64" Name="sigma_ip" NumberOfComponents="4" NumberOfTuples="198" format="appended" RangeMin="2184903.3215" RangeMax="3531311.2455" offset="228" />
+ </FieldData>
+ <Piece NumberOfPoints="36" NumberOfCells="22" >
+ <PointData>
+ <DataArray type="Float64" Name="MaterialForces" NumberOfComponents="2" format="appended" RangeMin="95.379865947" RangeMax="3880.30625" offset="1212" />
+ <DataArray type="Float64" Name="NodalForces" NumberOfComponents="2" format="appended" RangeMin="539550" RangeMax="15521225" offset="1628" />
+ <DataArray type="Float64" Name="displacement" NumberOfComponents="2" format="appended" RangeMin="0" RangeMax="0.0275" offset="1976" />
+ <DataArray type="Float64" Name="epsilon" NumberOfComponents="4" format="appended" RangeMin="0.0005" RangeMax="0.0005" offset="2480" />
+ <DataArray type="Float64" Name="sigma" NumberOfComponents="4" format="appended" RangeMin="2118783.7139" RangeMax="3531311.2455" offset="3452" />
+ </PointData>
+ <CellData>
+ <DataArray type="Float64" Name="nonequilibrium_stress" NumberOfComponents="4" format="appended" RangeMin="1731663.2249" RangeMax="3100953.7425" offset="4268" />
+ <DataArray type="Float64" Name="principal_stress_values" NumberOfComponents="3" format="appended" RangeMin="2184903.3215" RangeMax="3531311.2455" offset="4468" />
+ <DataArray type="Float64" Name="principal_stress_vector_1" NumberOfComponents="3" format="appended" RangeMin="1" RangeMax="1" offset="4724" />
+ <DataArray type="Float64" Name="principal_stress_vector_2" NumberOfComponents="3" format="appended" RangeMin="1" RangeMax="1" offset="4776" />
+ <DataArray type="Float64" Name="principal_stress_vector_3" NumberOfComponents="3" format="appended" RangeMin="1" RangeMax="1" offset="4828" />
+ </CellData>
+ <Points>
+ <DataArray type="Float64" Name="Points" NumberOfComponents="3" format="appended" RangeMin="0" RangeMax="55.901699437" offset="4880" />
+ </Points>
+ <Cells>
+ <DataArray type="Int64" Name="connectivity" format="appended" RangeMin="" RangeMax="" offset="5072" />
+ <DataArray type="Int64" Name="offsets" format="appended" RangeMin="" RangeMax="" offset="5272" />
+ <DataArray type="UInt8" Name="types" format="appended" RangeMin="" RangeMax="" offset="5384" />
+ </Cells>
+ </Piece>
+ </UnstructuredGrid>
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diff --git a/Tests/Data/Mechanics/InitialStates/soil_column_nonequilibrium_sigma_elementwise_ts_1_1.vtu b/Tests/Data/Mechanics/InitialStates/soil_column_nonequilibrium_sigma_elementwise_ts_1_1.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..663c1f3c0f73afd15439113271e11a999e254a7a
--- /dev/null
+++ b/Tests/Data/Mechanics/InitialStates/soil_column_nonequilibrium_sigma_elementwise_ts_1_1.vtu
@@ -0,0 +1,37 @@
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