1995 model - Violent shakes

My 1995 Buick Regal shakes violently at highway speeds. It has approx. 160,000 miles. It only occurs while maintaining speed or during slight acceleration, starting around 45 mph. It stops when I let off of the gas, or when I accelerate enough for the transmission to down shift. It takes about 2-3 seconds for the shaking to start, so I avoid it by holding the pedal for 2 seconds, then quickly but calmly releasing the pedal then reapplying pressure. Sounds annoying, but I've gotten used to it kinda like getting used to a standard transmission. Any ideas?