diff --git a/framework/doc/content/source/auxkernels/ElemExtraIDAux.md b/framework/doc/content/source/auxkernels/ElemExtraIDAux.md
new file mode 100644
index 000000000000..9d9f52094c1c
--- /dev/null
+++ b/framework/doc/content/source/auxkernels/ElemExtraIDAux.md
@@ -0,0 +1,11 @@
+# ElemExtraIDAux
+
+## Description
+
+This auxiliary kernel copies element integers into an auxiliary variable by evaluating the variable on quadrature points of any element with the element integer of the element.
+
+!syntax parameters /AuxKernels/ElemExtraIDAux
+
+!syntax inputs /AuxKernels/ElemExtraIDAux
+
+!syntax children /AuxKernels/ElemExtraIDAux
diff --git a/framework/doc/content/source/meshgenerators/FileMeshGenerator.md b/framework/doc/content/source/meshgenerators/FileMeshGenerator.md
index 57402f34a6ec..c1078c860eb7 100644
--- a/framework/doc/content/source/meshgenerators/FileMeshGenerator.md
+++ b/framework/doc/content/source/meshgenerators/FileMeshGenerator.md
@@ -23,6 +23,9 @@ supports reading and writing a large number of formats and could be extended to
 | .xda, .xdr  | libMesh formats |
 | .vtk, .pvtu | Visualization Toolkit |
 
+When reading a mesh file in Sandia's ExodusII format, users can use parameter *exodus_extra_element_integers* to load elemental variables for setting extra element integers of the mesh.
+The names of the extra element integers will be the same as the names of the element variables in the mesh file.
+
 ## Further FileMeshGenerator Documentation
 
 !syntax parameters /MeshGenerators/FileMeshGenerator
diff --git a/framework/include/auxkernels/ElemExtraIDAux.h b/framework/include/auxkernels/ElemExtraIDAux.h
new file mode 100644
index 000000000000..990b491c973d
--- /dev/null
+++ b/framework/include/auxkernels/ElemExtraIDAux.h
@@ -0,0 +1,31 @@
+//* This file is part of the MOOSE framework
+//* https://www.mooseframework.org
+//*
+//* All rights reserved, see COPYRIGHT for full restrictions
+//* https://github.com/idaholab/moose/blob/master/COPYRIGHT
+//*
+//* Licensed under LGPL 2.1, please see LICENSE for details
+//* https://www.gnu.org/licenses/lgpl-2.1.html
+
+#pragma once
+
+#include "AuxKernel.h"
+
+// Forward Declarations
+class ElemExtraIDAux;
+
+template <>
+InputParameters validParams<ElemExtraIDAux>();
+
+class ElemExtraIDAux : public AuxKernel
+{
+public:
+  static InputParameters validParams();
+
+  ElemExtraIDAux(const InputParameters & parameters);
+
+protected:
+  virtual Real computeValue() override;
+
+  const dof_id_type & _id;
+};
diff --git a/framework/src/auxkernels/ElemExtraIDAux.C b/framework/src/auxkernels/ElemExtraIDAux.C
new file mode 100644
index 000000000000..1cccfc3c364e
--- /dev/null
+++ b/framework/src/auxkernels/ElemExtraIDAux.C
@@ -0,0 +1,35 @@
+//* This file is part of the MOOSE framework
+//* https://www.mooseframework.org
+//*
+//* All rights reserved, see COPYRIGHT for full restrictions
+//* https://github.com/idaholab/moose/blob/master/COPYRIGHT
+//*
+//* Licensed under LGPL 2.1, please see LICENSE for details
+//* https://www.gnu.org/licenses/lgpl-2.1.html
+
+#include "ElemExtraIDAux.h"
+
+registerMooseObject("MooseApp", ElemExtraIDAux);
+
+defineLegacyParams(ElemExtraIDAux);
+
+InputParameters
+ElemExtraIDAux::validParams()
+{
+  InputParameters params = AuxKernel::validParams();
+  params.addRequiredParam<std::vector<ExtraElementIDName>>("extra_id_name",
+                                                           "The extra ID name in the mesh");
+  params.addClassDescription("Puts element extra IDs into an aux variable.");
+  return params;
+}
+
+ElemExtraIDAux::ElemExtraIDAux(const InputParameters & parameters)
+  : AuxKernel(parameters), _id(getElementID("extra_id_name"))
+{
+}
+
+Real
+ElemExtraIDAux::computeValue()
+{
+  return _id;
+}
diff --git a/framework/src/meshgenerators/FileMeshGenerator.C b/framework/src/meshgenerators/FileMeshGenerator.C
index 1b4145fa8a79..97ea346e83c1 100644
--- a/framework/src/meshgenerators/FileMeshGenerator.C
+++ b/framework/src/meshgenerators/FileMeshGenerator.C
@@ -12,6 +12,8 @@
 
 #include "libmesh/replicated_mesh.h"
 #include "libmesh/face_quad4.h"
+#include "libmesh/exodusII_io.h"
+#include "libmesh/mesh_communication.h"
 
 registerMooseObject("MooseApp", FileMeshGenerator);
 
@@ -23,6 +25,9 @@ FileMeshGenerator::validParams()
   InputParameters params = MeshGenerator::validParams();
 
   params.addRequiredParam<MeshFileName>("file", "The filename to read.");
+  params.addParam<std::vector<std::string>>(
+      "exodus_extra_element_integers",
+      "The variable names in the mesh file for loading extra element integers");
 
   return params;
 }
@@ -37,7 +42,25 @@ FileMeshGenerator::generate()
 {
   auto mesh = _mesh->buildMeshBaseObject();
 
-  mesh->read(_file_name);
+  bool exodus =
+      _file_name.rfind(".exd") < _file_name.size() || _file_name.rfind(".e") < _file_name.size();
+  bool has_exodus_integers = isParamValid("exodus_extra_element_integers");
+  if (exodus && has_exodus_integers)
+  {
+    if (mesh->processor_id() == 0)
+    {
+      ExodusII_IO io(*mesh);
+      io.set_extra_integer_vars(
+          getParam<std::vector<std::string>>("exodus_extra_element_integers"));
+      io.read(_file_name);
+    }
+    MeshCommunication().broadcast(*mesh);
+    mesh->prepare_for_use(false, false);
+  }
+  else if (!has_exodus_integers)
+    mesh->read(_file_name);
+  else
+    mooseError("\"exodus_extra_element_integers\" should be given only for Exodus mesh files");
 
   return dynamic_pointer_cast<MeshBase>(mesh);
 }
diff --git a/test/tests/meshgenerators/file_mesh_generator/exodus_file_mesh_with_id.i b/test/tests/meshgenerators/file_mesh_generator/exodus_file_mesh_with_id.i
new file mode 100644
index 000000000000..667b0bf7b852
--- /dev/null
+++ b/test/tests/meshgenerators/file_mesh_generator/exodus_file_mesh_with_id.i
@@ -0,0 +1,35 @@
+[Mesh]
+  [material_id_mesh]
+    type = FileMeshGenerator
+    file = mesh_with_material_id.e
+    exodus_extra_element_integers = material_id
+  []
+[]
+
+[AuxVariables]
+  [material_id]
+    family = MONOMIAL
+    order = CONSTANT
+  []
+[]
+
+[AuxKernels]
+  [set_material_id]
+    type = ElemExtraIDAux
+    variable = material_id
+    extra_id_name = material_id
+  []
+[]
+
+[Problem]
+  kernel_coverage_check = false
+  solve = false
+[]
+
+[Executioner]
+  type = Steady
+[]
+
+[Outputs]
+  exodus = true
+[]
diff --git a/test/tests/meshgenerators/file_mesh_generator/gold/exodus_file_mesh_with_id_out.e b/test/tests/meshgenerators/file_mesh_generator/gold/exodus_file_mesh_with_id_out.e
new file mode 100644
index 000000000000..9b8b6fcfdab0
Binary files /dev/null and b/test/tests/meshgenerators/file_mesh_generator/gold/exodus_file_mesh_with_id_out.e differ
diff --git a/test/tests/meshgenerators/file_mesh_generator/mesh_with_material_id.e b/test/tests/meshgenerators/file_mesh_generator/mesh_with_material_id.e
new file mode 100644
index 000000000000..43098b91cf9e
Binary files /dev/null and b/test/tests/meshgenerators/file_mesh_generator/mesh_with_material_id.e differ
diff --git a/test/tests/meshgenerators/file_mesh_generator/tests b/test/tests/meshgenerators/file_mesh_generator/tests
index 30ca80b88e11..c928bb50c2e0 100644
--- a/test/tests/meshgenerators/file_mesh_generator/tests
+++ b/test/tests/meshgenerators/file_mesh_generator/tests
@@ -11,4 +11,14 @@
     design = 'meshgenerators/FileMeshGenerator.md'
     issues = '#11640'
   [../]
+  [./extra_integer_test]
+    type = 'Exodiff'
+    input = 'exodus_file_mesh_with_id.i'
+    exodiff = 'exodus_file_mesh_with_id_out.e'
+    recover = false
+
+    requirement = 'The system shall have the ability to assign element extra integers with elemental variables in an Exodus mesh file.'
+    design = 'meshgenerators/FileMeshGenerator.md'
+    issues = '#14916'
+  [../]
 []