They sell things that you clip to the underside of the fitted sheets to help hold them on. Like a one-inch wide strip if elastic a couple inches long with a clip on each end.

As a kid my sheets always came off--now they stay on great. Maybe I've just been lucky in getting the right sizes!!
"I don't know! I don't know why I did it, I don't know why I enjoyed it, and I don't know why I'll do it again!" -BART SIMPSON