Measure the width and height of the futon mattress. Write these measurements down. Measure the thickness of the futon mattress. Divide this measurement in half and write it down.
Add 2-1/2" to each measurement.
Trim the sheets, if needed, to match the numbers from Step 2, to make sure the cover will fit snugly. Make sure to leave the hem (pre-finished edge) on one of the short ends of each sheet intact.
Place the sheets right sides together and pin them together along three sides, leaving the hemmed short ends open.
Sew the sheets together along three sides using a 5/8" seam allowance. Turn the sheets right-side out.
Cut strips of hook and loop tape about 3" long. Cut enough pieces to cover the open end of the cover, with no more than 3" between the pieces.
Position the hook sides of the pieces along one of the open edges and pin them to the sheet. Position the loop sides of the pieces along the other edge, making sure to line them up with the hook sides. Pin the loop pieces to the sheet.
Stitch around the edges of each piece of hook and loop tape. You may want to use a zigzag stitch if your sewing machine has one, so that the stitches will overlap the edges and hold the hook and loop tape in place.
Slide the cover over the mattress. Fasten the open end together using the hook and loop tape.