Your favorite pair of sandals is out of commission because of a broken strap. If it's the elastic strap over the heel, you might think that they're useless and fit only for the trash. Know that you can fix them and get more wear out of them. The repair is a patch extension repair. It is also sometimes called a "jump strap" repair. A new piece of elastic is sewn over the snapped elastic ends.
Purchase a length of good elastic the same width as the broken strap. You can get elastic from a shoe repair shop. You can also steal a piece of elastic from another shoe in your wardrobe. It's important for the replacement elastic to be the same color as the broken elastic so the repair is invisible.
Secure the broken ends of the shoe strap using super glue. Make a straight cut on each end and glue the strap seams and ends closed to strengthen the original straps as much as possible before affixing the extension repair elastic piece. Also, glue the new strip ends and seams to make them as strong as possible.
Working on one end of the broken strap, sew the new repair strap strip onto the broken strap, overlapping about 1/8 inch beyond the broken strap end. Use a heavy-duty sewing machine needle or heavy-duty needle with plastic thread in a matching color, which can be found in fabric stores, if doing a hand sew. Make several passes back and forth with the machine or the needle to make the sewn stitching as strong as possible.
Before repairing the other end of the strap, put the sandal on to determine the appropriate length of elastic needed. You'll want to make certain there isn't too much elastic added to the strap so that the fit of the sandal is compromised.
Once you're comfortable with where the repair should be made, use a paper clip to mark the location. You may need to cut the elastic if too long and re-glue the ends and seam of the elastic extension with super glue. Stretch the end of the elastic over the broken strap end and sew as before on a machine or by hand. The repair should be virtually invisible.
References
Repairing an Elastic Strap