What causes the 2002 Toyota Solara to shake when accelerating?

There could be many causes ranging from a bad spark plug that fails when combustion chamber pressures rise to frozen half shafts. If the vibration is only felt when you accelerate from the same speed or when passing through the same speed you might suspect tire imbalance.

Of course if it's a Generation I Solara convertible then the answer is "they all do it" to some extent. The early ragtop is known for its shimmies and shakes so the issue could even be a road surface.

Hopefully someone who owns a Gen I Solara will come along with an edit saying "mine did that and it was ......"

Cheers