I played for about 15 minutes today and all of a sudden I realize that my amp smells like it's burning or like plastic was melting. It's a Peavey Classic 30 tube amp. Does anybody know what the problem is? Thanks
The smell of burning or melting plastic usually means, well, something made of plastic is burning or melting!

Crack it open and have a look. Find out what appears to be melting and get back to us. Just make sure the amp is unplugged, and watch out for the electrolytic caps - they might carry a high voltage charge for a while after the amp is turned off.
It was a bit dusty so that could be it. I also bought it used so the tubes could be going bad by now. I don't wanna crack it open, really. I don't know jack about electronics and would probably break something.

EDIT: Is there any other way to tell it's the tubes?
Describe the smell. Different things inside your amp smell differently when they go bad. Natural tube smell is warm and kind of like old books or grease. Other stuff smells different. So...what does it smell like?
possibly just dust on a hot bit

possibly a seriously dangerous fault
Get off this damn forum and play your damn guitar.