Well that's a little bizarre. Here's a few things to try:
Make sure your Firefox is updated to the most recent version.
Try it in another browser (Internet Explorer, Google Chrome, Opera, etc...), and if it crashes in one of those too, then it's probably your computer, not Firefox.
If it doesn't crash in one of those other browsers, then try uninstalling and reinstalling Firefox.
Are you trying to upload directly to the site? Or are you using some sort of Rapidshare toolbar?
Upload directly to the site...
Try using their toolbar:
http://rapidsharetoolbar.com/
I haven't used this myself, so I don't know, but I'm assuming it has an upload option.
Did you try those other things I suggested? What are the results?
thats doesnt seems to work...
Then it's something wrong with your computer. Try clearing your cache, deleting all your cookies, and running a virus scan. After you do all that, try again and let me know the results.