Cook pasta in large pot of boiling water until al dente. Rinse under cold water and drain.
Mix chopped carrots, celery, cucumber, green pepper, tomatoes and onion together in large bowl.
Combine cooled pasta and vegetables together in large bowl. Pour Italian dressing over mixture, add Parmesan cheese and mix well.
Chill for one hour before serving.
Parmesan cheese is not truly vegetarian, as it contains animal rennet. To make this dish 100% vegetarian, omit the cheese or find a suitable vegetarian substitute made without animal rennet. In supermarkets look for the 'parmesan style hard cheeses' which are suitable for vegetarians.