We will use a deformer, the scale tool, and keyframing to bounce a ball so that it squishes on the ground and then stretches as it bounces up. (You can left click on any image below to blow it up.) The ball. First we create a NURBS ball. The Squish Deformer. Then we select the ball and create a Squash deformer from Create Deformers (on the Main Menu with the Main Menu Selector set to Animation).
Squish the ball. We then place the ball on the lower plane and then select the deformer. We use the move tool to lower the pink deformer handle inside the ball to squish the ball.
Keyframe the ball. We then keyframe the ball to go up and down over a series of at least 75 frames (so we can easily see it move and deform). This is how we set the keyframes: Stretch the ball. We start at the top and set the first keyframe there (with the s key). But before we set the keyframe, we use the scale tool to stretch the ball out top-to-bottom. Bounce the ball. Then we go to frame 30 or so, move the ball to the ground (and the deformer will automatically squish it for us). We set the second keyframe it there. Stretch the ball. Then we keyframe it at the top again, at perhaps keyframe 75. But again, before we set the keyframe, we use the scale tool to stretch it out top-to-bottom again. Run the scene. We see it fall and squish, then bounce and stretch. Maya even makes it stretch gradually as it moves upward.