diff --git a/doc/source/whatsnew/v1.0.0.rst b/doc/source/whatsnew/v1.0.0.rst
index b015f439935cb..8a60fd2062b61 100644
--- a/doc/source/whatsnew/v1.0.0.rst
+++ b/doc/source/whatsnew/v1.0.0.rst
@@ -535,6 +535,7 @@ Reshaping
 - Bug :meth:`Series.pct_change` where supplying an anchored frequency would throw a ValueError (:issue:`28664`)
 - Bug where :meth:`DataFrame.equals` returned True incorrectly in some cases when two DataFrames had the same columns in different orders (:issue:`28839`)
 - Bug in :meth:`DataFrame.replace` that caused non-numeric replacer's dtype not respected (:issue:`26632`)
+- Bug in :func:`melt` where supplying mixed strings and numeric values for ``id_vars`` or ``value_vars`` would incorrectly raise a ``ValueError`` (:issue:`29718`)
 
 Sparse
 ^^^^^^
diff --git a/pandas/core/reshape/melt.py b/pandas/core/reshape/melt.py
index 4cba52c5cd651..8e9edfa5f1409 100644
--- a/pandas/core/reshape/melt.py
+++ b/pandas/core/reshape/melt.py
@@ -11,6 +11,7 @@
 from pandas.core.dtypes.missing import notna
 
 from pandas.core.arrays import Categorical
+import pandas.core.common as com
 from pandas.core.frame import DataFrame, _shared_docs
 from pandas.core.indexes.base import Index
 from pandas.core.reshape.concat import concat
@@ -47,7 +48,7 @@ def melt(
         else:
             # Check that `id_vars` are in frame
             id_vars = list(id_vars)
-            missing = Index(np.ravel(id_vars)).difference(cols)
+            missing = Index(com.flatten(id_vars)).difference(cols)
             if not missing.empty:
                 raise KeyError(
                     "The following 'id_vars' are not present"
@@ -69,7 +70,7 @@ def melt(
         else:
             value_vars = list(value_vars)
             # Check that `value_vars` are in frame
-            missing = Index(np.ravel(value_vars)).difference(cols)
+            missing = Index(com.flatten(value_vars)).difference(cols)
             if not missing.empty:
                 raise KeyError(
                     "The following 'value_vars' are not present in"
diff --git a/pandas/tests/reshape/test_melt.py b/pandas/tests/reshape/test_melt.py
index 4521f1bbf1a08..d6946ea41ed84 100644
--- a/pandas/tests/reshape/test_melt.py
+++ b/pandas/tests/reshape/test_melt.py
@@ -317,6 +317,22 @@ def test_melt_missing_columns_raises(self):
         ):
             multi.melt(["A"], ["F"], col_level=0)
 
+    def test_melt_mixed_int_str_id_vars(self):
+        # GH 29718
+        df = DataFrame({0: ["foo"], "a": ["bar"], "b": [1], "d": [2]})
+        result = melt(df, id_vars=[0, "a"], value_vars=["b", "d"])
+        expected = DataFrame(
+            {0: ["foo"] * 2, "a": ["bar"] * 2, "variable": list("bd"), "value": [1, 2]}
+        )
+        tm.assert_frame_equal(result, expected)
+
+    def test_melt_mixed_int_str_value_vars(self):
+        # GH 29718
+        df = DataFrame({0: ["foo"], "a": ["bar"]})
+        result = melt(df, value_vars=[0, "a"])
+        expected = DataFrame({"variable": [0, "a"], "value": ["foo", "bar"]})
+        tm.assert_frame_equal(result, expected)
+
 
 class TestLreshape:
     def test_pairs(self):