Geez, it's called a Bungie Cord.
I thought it was a Bungie Cord but then thought about a Bungie Cord for jumping off bridges with it around your ankles.
Stretchy Thing sounded less stupid than the completely wrong term.
A couple of years ago I gave Mr. RightField a large bag of about 40 assorted bungee cords, along with a sweater, shoes, after shave, etc, for Christmas. I bought them in a moment of what-else-can-I-get-him desperation in the Home Depot. He STILL raves incessantly about his wonderful supply of bungee cords; he loves them almost as much as his various rolls of duct tape.