diff --git a/jupytext/cell_reader.py b/jupytext/cell_reader.py
index eee96d51e..ef786db70 100644
--- a/jupytext/cell_reader.py
+++ b/jupytext/cell_reader.py
@@ -270,6 +270,11 @@ def metadata_and_language_from_option_line(self, line):
                 self.metadata['region_name'] = region_name
         elif self.start_code_re.match(line):
             self.language, self.metadata = self.options_to_metadata(self.start_code_re.findall(line)[0])
+            # Cells with a .noeval attribute are markdown cells #347
+            if self.metadata.get('.noeval', '') is None:
+                self.cell_type = 'markdown'
+                self.metadata = {}
+                self.language = None
 
     def options_to_metadata(self, options):
         if isinstance(options, tuple):
@@ -306,12 +311,24 @@ def find_cell_end(self, lines):
                 if in_indented_code_block or in_explicit_code_block:
                     continue
 
-                if self.start_code_re.match(line) or self.start_region_re.match(line):
+                if self.start_region_re.match(line):
+                    if i > 1 and prev_blank:
+                        return i - 1, i, False
+                    return i, i, False
+
+                if self.start_code_re.match(line):
+                    # Cells with a .noeval attribute are markdown cells #347
+                    _, metadata = self.options_to_metadata(self.start_code_re.findall(line)[0])
+                    if metadata.get('.noeval', '') is None:
+                        in_explicit_code_block = True
+                        prev_blank = 0
+                        continue
+
                     if i > 1 and prev_blank:
                         return i - 1, i, False
                     return i, i, False
 
-                if self.non_jupyter_code_re and self.non_jupyter_code_re.match(line):
+                if self.non_jupyter_code_re.match(line):
                     in_explicit_code_block = True
                     prev_blank = 0
                     continue
diff --git a/tests/test_read_simple_markdown.py b/tests/test_read_simple_markdown.py
index 8fd514ff0..1a49563dd 100644
--- a/tests/test_read_simple_markdown.py
+++ b/tests/test_read_simple_markdown.py
@@ -455,3 +455,34 @@ def test_inactive_cell_using_tag(text='''```python tags=["active-md"]
     compare_notebooks(nb, expected)
     text2 = jupytext.writes(nb, 'md')
     compare(text2, text)
+
+
+def test_inactive_cell_using_noeval(text='''This is text
+
+```python .noeval
+# This is python code.
+# It should not become a code cell
+```
+'''):
+    expected = new_notebook(cells=[new_markdown_cell(text[:-1])])
+    nb = jupytext.reads(text, 'md')
+    compare_notebooks(nb, expected)
+    text2 = jupytext.writes(nb, 'md')
+    compare(text2, text)
+
+
+def test_noeval_followed_by_code_works(text='''```python .noeval
+# Not a code cell in Jupyter
+```
+
+```python
+1 + 1
+```
+''', expected=new_notebook(cells=[new_markdown_cell('''```python .noeval
+# Not a code cell in Jupyter
+```'''),
+                                  new_code_cell('1 + 1')])):
+    nb = jupytext.reads(text, 'md')
+    compare_notebooks(nb, expected)
+    text2 = jupytext.writes(nb, 'md')
+    compare(text2, text)