How do I keep my mattress from sliding on the box spring?

Carpet grips work for me. The $ store has them about mat size. You can put one at each corner of your bed

Natural Rubber Rug Pad:

All rubber or polymer /polyester coated rug pads coated pads are usually a minimum 1/8″ thick and have holes. These holes have a honey comb or waffle like texture that act as a void where the mattress is not coming in contact with the rubber potentially causing less grip. Sizes are commonly available in 4 x 6, 5 x 8, and 8 x 10 sheets. Keep in mind the best underlay should be only slightly smaller than the mattress size itself which will be most affect at keeping it stuck in place.

Felt Rug Pad:

One side is made with a thick felt rug pad and includes a rubber backing designed to grip. They are offered in large sheets that come 4 x 6, 5 x 8, and 8 x 10. Ideally you want the underlayment to be 1 inch smaller than the mattress just as if you were installing it under an area rug. Trimming them to size is easy. Non-slide rug pads are typically 1/4″ thick, where most rubber ones are half of that at 1/8″. The thicker felt pads include a solid rubber backing which will be most effective at keeping the mattress from sliding and locked into place.

Shelf liner:

Shelf or drawer lining is a cheap low cost version of the natural rubber pad version mentioned earlier. Rubber shelf/drawer liner is a decent idea people frequently try when they are trying to save money. Lower cost to produce and the fact that it comes in small rolls helps keeps cost down. For some people a couple rolls will get the job done. The rolls are strips usually around 12 and 24 inches wide. Lengths vary greatly but 48” and 60” inches long are common. For mattresses that do not slide around too bad this can be very affective. It is recommended to add multiple pieces until sliding is minimized or stopped. For bad sliding problems this usually is not enough to keep the mattress in place and secure it from sliding around.

Double sided carpet tape:

Some people say they have used double sided carpet tape.

I had a disabled client who used to thrash her mattress off at night. So I got 2 rachet straps big enough to go around her queen mattress at top and bottom. Just put the fitted sheet over them. using those corner sheet straps. Never fell off again. Look in store car department.

Ours did that, hubby attached brackets at end of bed one on each corner.

Another solution would be to glue (E-6000) velcro strips on the top of the box springs with the opposite velcro strips on the bottom of the mattress. That should keep it in place.