diff --git a/src/FileFormats/MPS/read.jl b/src/FileFormats/MPS/read.jl
index a3436184e1..f623c457d5 100644
--- a/src/FileFormats/MPS/read.jl
+++ b/src/FileFormats/MPS/read.jl
@@ -776,19 +776,24 @@ end
 
 # TODO: handle multiple RHS vectors.
 function parse_rhs_line(data::TempMPSModel{T}, items) where {T}
-    if length(items) == 3
+    if length(items) == 2
+        # [row name] [value]
+        parse_single_rhs(data, items[1], parse(T, items[2]), items)
+    elseif length(items) == 3
         # [rhs name] [row name] [value]
-        rhs_name, row_name, value = items
-        parse_single_rhs(data, row_name, parse(T, value), items)
+        parse_single_rhs(data, items[2], parse(T, items[3]), items)
+    elseif length(items) == 4
+        # [row name 1] [value 1] [row name 2] [value 2]
+        parse_single_rhs(data, items[1], parse(T, items[2]), items)
+        parse_single_rhs(data, items[3], parse(T, items[4]), items)
     elseif length(items) == 5
         # [rhs name] [row name 1] [value 1] [row name 2] [value 2]
-        rhs_name, row_name_1, value_1, row_name_2, value_2 = items
-        parse_single_rhs(data, row_name_1, parse(T, value_1), items)
-        parse_single_rhs(data, row_name_2, parse(T, value_2), items)
+        parse_single_rhs(data, items[2], parse(T, items[3]), items)
+        parse_single_rhs(data, items[4], parse(T, items[5]), items)
     else
         _throw_parse_error(
             data,
-            "Malformed RHS line: expected three or five fields.",
+            "Malformed RHS line: expected 2, 3, 4, or 5 fields.",
         )
     end
     return
diff --git a/test/FileFormats/MPS/failing_models/rhs_malformed.mps b/test/FileFormats/MPS/failing_models/rhs_malformed.mps
index b56683624a..1f0f470860 100644
--- a/test/FileFormats/MPS/failing_models/rhs_malformed.mps
+++ b/test/FileFormats/MPS/failing_models/rhs_malformed.mps
@@ -6,5 +6,5 @@ COLUMNS
     x         c         1
     x         d         1
 RHS
-    rhs       d         con      1
+    foo
 ENDATA
diff --git a/test/FileFormats/MPS/failing_models/rhs_malformed2.mps b/test/FileFormats/MPS/failing_models/rhs_malformed2.mps
deleted file mode 100644
index 0e279c9f56..0000000000
--- a/test/FileFormats/MPS/failing_models/rhs_malformed2.mps
+++ /dev/null
@@ -1,10 +0,0 @@
-NAME
-ROWS
- N  c
- G  d
-COLUMNS
-    x         c         1
-    x         d         1
-RHS
-    rhs       con1      1
-ENDATA
diff --git a/test/FileFormats/MPS/test_MPS.jl b/test/FileFormats/MPS/test_MPS.jl
index 369f1fa0c5..6ed2e9aa84 100644
--- a/test/FileFormats/MPS/test_MPS.jl
+++ b/test/FileFormats/MPS/test_MPS.jl
@@ -1786,6 +1786,50 @@ function test_parse_header()
     return
 end
 
+function test_issue_2941()
+    src = """
+    NAME
+    ROWS
+     E  c2
+     E  c3
+     E  c4a
+     E  c4b
+     E  c5a
+     E  c5b
+    COLUMNS
+        x         c2      1.0
+        x         c3      1.0
+        x         c4a     1.0
+        x         c4b     1.0
+        x         c5a     1.0
+        x         c5b     1.0
+    RHS
+         c2       1.1
+     rhs c3       1.2
+         c4a      1.3      c4b           1.4
+     rhs c5a      1.5      c5b           1.6
+    BOUNDS
+     LO bounds    x         1
+    ENDATA
+    """
+    model = MPS.Model()
+    read!(IOBuffer(src), model)
+    dest = MOI.Utilities.Model{Float64}()
+    MOI.copy_to(dest, model)
+    for (c_name, rhs) in [
+        "c2" => 1.1,
+        "c3" => 1.2,
+        "c4a" => 1.3,
+        "c4b" => 1.4,
+        "c5a" => 1.5,
+        "c5b" => 1.6,
+    ]
+        ci = MOI.get(dest, MOI.ConstraintIndex, c_name)
+        @test MOI.get(dest, MOI.ConstraintSet(), ci).value == rhs
+    end
+    return
+end
+
 end  # TestMPS
 
 TestMPS.runtests()