All of a sudden my car shakes violently...Doh!

Drove my '67 cuda this afternoon and when I accelerate and travel in
excess of 30 mph, the entire car shakes violently and I do mean
violently. It only happens when I accelerate. When I step off the
accelerator, the trembling stops. Any ideas...unbalanced tires,
shot u-joints, attempted alien abduction?

Rob