diff --git a/src/problems.jl b/src/problems.jl
index a303719..85ab797 100644
--- a/src/problems.jl
+++ b/src/problems.jl
@@ -252,3 +252,33 @@ end
 function push!(problem::Problem, element)
     push!(problem.elements, element)
 end
+
+""" Find dofs corresponding to nodes. """
+function find_dofs_by_nodes(problem::Problem, nodes)
+    dim = get_unknown_field_dimension(problem)
+    return find_dofs_by_nodes(dim, nodes)
+end
+function find_dofs_by_nodes(dim::Int, nodes)
+    dofs = Int64[]
+    for node in nodes
+        for j=1:dim
+            push!(dofs, dim*(node-1)+j)
+        end
+    end
+    return dofs
+end
+
+""" Find nodes corresponding to dofs. """
+function find_nodes_by_dofs(problem::Problem, dofs)
+    dim = get_unknown_field_dimension(problem)
+end
+function find_nodes_by_dofs(dim, dofs)
+    nodes = Int64[]
+    for dof in dofs
+        j = Int(ceil(dof/dim))
+        j in nodes && continue
+        push!(nodes, j)
+    end
+    return nodes
+end
+
diff --git a/test/test_node_dof_mapping.jl b/test/test_node_dof_mapping.jl
new file mode 100644
index 0000000..4b5c06b
--- /dev/null
+++ b/test/test_node_dof_mapping.jl
@@ -0,0 +1,21 @@
+# This file is a part of JuliaFEM.
+# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
+
+using JuliaFEM.Test
+
+using JuliaFEM.Core: find_dofs_by_nodes, find_nodes_by_dofs
+
+@testset "find dofs given a set of nodes" begin
+    nodes = [1, 3]
+    dim = 3
+    dofs = find_dofs_by_nodes(dim, nodes)
+    @test dofs == [1, 2, 3, 7, 8, 9]
+end
+
+@testset "find nodes given a set of dofs" begin
+    dofs = [2, 8, 9]
+    dim = 3
+    nodes = find_nodes_by_dofs(dim, dofs)
+    @test nodes == [1, 3]
+end
+