I do mine on the elliptical all the time. If you've never done it before, you'll be surprised how hard it is and you'll need to build up your interval times.
To start off, try this:
2 min warm up/steady state
30 sec sprint as fast as you can
2 min steady state
30 sec sprint
keep repeating for a total of 20 minutes. If you do it right, after 20 minutes you'll feel like dying.
As you progress you can increase your sprint time to 40, then 60 seconds. Just be sure to pay attention to your HR and how you are feeling. You can also change it up and instead of sprint as fast as you can, you can increase the resistance for that shorter time period.