GM-GMC: Chevy 4x4 vibrating during acceleration, shock absorber, steering stabilizer

Question
I have a 94, chevy, 1/2 ton, 4 x 4, 1500, it's got a 350 engine and about 200,000 miles. It's vibrating during acceleration only but in both 2 and 4 wheel drive. The vibration is most felt through the steering wheel. The front end seems tight, there's no play in the front suspention or wheels. The transmission was rebuilt at around 160,000 miles and I've replaced the main drive shaft u-joints. The output shafts of the trans-axle have alot of play but then they always have, not sure what normal. Have an idea of what's causing the vibration???

Answer
If it vibrates ONLY during acceleration, I would take a look at the motor mounts and transmission mounts.  With that many miles on the powertrain, one or more of those mounts are likely worn out or broken.
You may also have a worn out steering stabilizer, if your vehicle is equipped with one.  It is a horizonatally mounted shock absorber that connects to the steering linkage.