Why does your Chevy 350 engine stutter when you accelerate?

There could be many causes. It would be easier to answer with more information, What year 350?, fuel injection or carburetor?

Water in gas

Low fuel pressure

Vacuum leak

Bad spark plugs

bad plug wires

bad distributor cap

bad coil

Detonation

Bad timing

bad camshaft

are a few items that would make it happen

I hope this helps