Unlike a motion tween, a shape tween requires that you start and end with a native Flash shape, rather than a symbol. Flash uses the vector information of the shape (or shapes) in the start keyframe and the changed vector information of the shape in the end keyframe to construct intermediate frames. Shape tweens can be used to morph objects from one shape to another, or they can be used to quickly set up a tween when one shape, or a group of shapes, shifts position or size or color (without having to change the content to a symbol first). Shape tweens often don't work well when the shape in the start keyframe is very different (especially in number of vectors that define it) from the shape in the last frame. Here's an example of using a shape tween to provide an animated cartoony bounce:
Open a new 500x200 movie and draw a floor in one layer and a round ball in the air in the layer above. Extend the timeline to frame 16. Put a keyframe in frame 8 and another in frame 16. In keyframe 10, drag the ball down over the floor. Click in frame 1 and choose Shape from the Tween box in the Properties panel. Click frame 8 and repeat. You should see arrows over green shading in the timeline, which represents a shape tween. Control, Test Movie should produce something like:
Let's see if we can make the bouncing a bit more convincing. Click frame 1 and set the Ease to 100 (Ease Out) in the properties panel. Do the same for frame 8. Turn on onion skin outlines to see that the end frames of the tween now appear closer together than the beginning frames. Control, Test Movie to see.

Adding a little shape change to the ball will emphasize its bounce even more. In frame 1, use the transform tool to squash the ball up a bit vertically. Move the keyframe in frame 8 back to frame 5. Add a keyframe in frame 6. In that frame, squash the ball vertically and spread it horizontally (making sure the ball ends up lower in this frame than in frame 5 -- this is the bottom point of its bounce). Put a blank keyframe in frame 7. Copy the content of frame 5 into frame 7 (using cmd-shift-v to paste in place). Add a keyframe in frame 14. Squish the ball horizontally and spread it vertically. Move keyframes or add extra frames if desired (we put another frame in after frameNow the bounce should look something like:
Finally, the ball can be made to bounce across the screen by creating a bouncingball movieclip and motion tweening it across the stage. The steps to do that are: cut the frames of the ball layer onto the clipboard (select frames, right-click, Cut Frames), create new movieclip bouncingball, click in frame 1 and paste the frames into it. Go back to the main movie (scene1) and drag the new movieclip from the library into the ball layer and extend the timeline for both layers out (I extended to frame 85, with the frame rate changed to 20 fps). Put a keyframe in the last frame of the ball layer, move the ball offstage at far right, shrink it, and set its tint to 80% of the floor color (or any other modifications you want to make to make it look as though the ball is bouncing off into the distance. Turn motion tweening on in frame 1, with Ease Out if desired.
Discussed on this page:
shape tweens, cartoon bouncing ball, onion skin outlines
Other Resources
The idea for the bouncing ball in this example came from the book Flash 5 Cartoons and Games, which, although it was written when Flash 5 came out, is still a wonderful source of cartoon tips, from walk cycles, character animation and lip-syncing to game code.
Another book with good descriptions of weight in movement and other animation techniques (not Flash-specific but has been recommended more than any other animation book I know of) is The Animator's Workbook by Tony White.
You can modify a shape tween by adding Shape Hints (see the Flash help for examples), but doing so can sometimes be an exercise in frustration. One alternative (which leads to a larger file size but more control over the tween) is to create a blend of two objects in Illustrator and export it as a keyframe sequence for use in Flash.