diff --git a/src/read_aster_mesh.jl b/src/read_aster_mesh.jl
index 189586c..f81f2a9 100644
--- a/src/read_aster_mesh.jl
+++ b/src/read_aster_mesh.jl
@@ -98,9 +98,19 @@ function get_element_sets(med::MEDFile, mesh_name::String)::Dict{Int64, Vector{S
     if !haskey(mesh, "ELEME")
         return element_sets
     end
-    for (k, v) in mesh["ELEME"]
-        elset_id = parse(Int, split(k, '_')[2])
-        element_sets[elset_id] = collect(to_ascii(d) for d in v["GRO"]["NOM"])
+    elset_keys = sort(collect(keys(mesh["ELEME"])))
+    for (i, k) in enumerate(elset_keys)
+        v = mesh["ELEME"][k]
+        if startswith(k, "FAM") # exported from Salome
+            elset_id = parse(Int, split(k, '_')[2])
+        else # exported from Gmsh
+            elset_id = -i
+        end
+        if !isempty(v)
+            element_sets[elset_id] = map(strip, collect(to_ascii(d) for d in v["GRO"]["NOM"]))
+        else
+            element_sets[elset_id] = [""]
+        end
     end
     return element_sets
 end
@@ -110,9 +120,9 @@ function get_nodes(med::MEDFile, nsets::Dict{Int, Vector{String}}, mesh_name::St
     @assert length(increments) == 1
     increment = first(increments)
     nodes = med.data["ENS_MAA"][mesh_name][increment]["NOE"]
-    node_ids = nodes["NUM"]
     nset_ids = nodes["FAM"]
-    nnodes = length(node_ids)
+    nnodes = length(nset_ids)
+    node_ids = get(nodes, "NUM", collect(1:nnodes))
     node_coords = nodes["COO"]
     dim = round(Int, length(node_coords)/nnodes)
     node_coords = reshape(node_coords, nnodes, dim)'
@@ -136,8 +146,8 @@ function get_connectivity(med::MEDFile, elsets::Dict{Int64, Vector{String}}, mes
     for eltype in keys(all_elements)
         elements = all_elements[eltype]
         elset_ids = elements["FAM"]
-        element_ids = elements["NUM"]
-        nelements = length(element_ids)
+        nelements = length(elset_ids)
+        element_ids = get(elements, "NUM", collect(1:nelements))
         element_connectivity = elements["NOD"]
         element_dim = round(Int, length(element_connectivity)/nelements)
         element_connectivity = reshape(element_connectivity, nelements, element_dim)'
diff --git a/test/runtests.jl b/test/runtests.jl
index 2e49463..a4caa8e 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -8,6 +8,7 @@ include(joinpath("..", "docs", "make.jl"))
 @testset "AsterReader.jl" begin
     include("test_read_aster_mesh.jl")
     include("test_read_aster_results.jl")
+    include("test_read_gmsh_med.jl")
 end
 
 include(joinpath("..", "docs", "deploy.jl"))
diff --git a/test/test_read_gmsh_med.jl b/test/test_read_gmsh_med.jl
new file mode 100644
index 0000000..1b8c3c7
--- /dev/null
+++ b/test/test_read_gmsh_med.jl
@@ -0,0 +1,12 @@
+# This file is a part of JuliaFEM.
+# License is MIT: see https://github.com/JuliaFEM/AsterReader.jl/blob/master/LICENSE
+
+using FEMBase, Test, AsterReader
+using AsterReader: aster_parse_nodes, aster_read_mesh, MEDFile, get_element_sets
+
+datadir = first(splitext(basename(@__FILE__)))
+
+@testset "test med file exported from gmsh, issue #16" begin
+    mesh_file = joinpath(datadir, "t1.med")
+    mesh = aster_read_mesh(mesh_file)
+end
diff --git a/test/test_read_gmsh_med/t1.med b/test/test_read_gmsh_med/t1.med
new file mode 100644
index 0000000..b82478d
Binary files /dev/null and b/test/test_read_gmsh_med/t1.med differ