I have a 3 year old HE3 Kenmore Elite Dryer-Gas. When I attempt to start a cycle it throws the circuit breaker, sometimes immediately other times after a few minutes. If I let it sit for a couple of minutes it will run for a "short" time(pun not intended). I Have moved the electrical source to exclude a bad plug or breaker... help obviously paid way too much not fix it... thank you for any troubleshooting tips...

What is the dryer rated at should be on the unit and what size breakers are you using?
Did you try it without any clothes in it? Did it work for 3 years in the same config?
You could disconnect the heating element and run it to see if it still blows breaker. Just a thought