2001 Toyota Corolla Shaking when I excelerate.

I would first check the tires to make sure they have correct psi, of proper wear, and type for the car. Sometimes a tire's belt can shift and cause this problem. You can check this simply by rotating each tire and watch it to make sure it doesn't wobble and spins right. (Watch out for loose dirt and pebbles) Tire balancing will tell you if the tire and the rim are true and also if they need to be fitted with weights. Another quick test is to rotate the tires and see if it changes anything. Good luck