How do I ID a 340?

There should be some numbers stamped into the block on the front, just under the driver's side head that will have information about the block. One part will be the engine size. The stamping is faint sometimes, and can be filled with paint. Some brake cleaner and a rag can help a bunch. And a flashlight.

The only other external ID is the casting numbers on the side of the block, which you've already said that you can't see.