One of the problems with dressing an adjustable bed mattress, is that they tend to move more than the average sheet can accommodate them.

You can see here how the center portion of the sheet wants to follow a straight line, instead of the curve of the mattress, and ends up popping free.

The solution is actually very simple.  As you can see, we've altered the problem portion of the sheet with extra width, in the form of these "wings" and removed the elastic in that area.
   Now, we simply tuck in this extra fabric, which will be held in place by the increasing weight of the mattress as it is adjusted.  The higher it is adjusted, the more firmly it holds.
Then, as you can see here, the problem is solved.

For obvious reasons, we would recommend wings, as well as Anchor-Tite Corners on every fitted sheet for adjustable beds.