What could cause your engine to shake when you shift to reverse on a automatic transmission?

It's difficult to get a feel for what you mean when you say your engine shakes. Do you mean a regular shake? If that's the case it might be a bad valve, sparkplug, plug wire or injector. If you mean that the engine moves quite a distance when you put it in reverse, but then comes back, it could be a motor mount. Please feel free to send an e-mail directly if you want to discuss the situation further.