Which Fallout is this? I actually had that problem with Fallout 3 (still do, actually.) With me, I just kept ejecting and re-inserting until it would read. Got really annoying, but one it's installed you can bypass the disck-check by going directly to the program shortcut and not the auto-run one.
If you're talking about Fallout 1 or 2, then I'm not sure. Haven't had that problem, but I'd assume it would be the same.
Also, you could probably try to contact customer support and tell them you have a defective disk - they might let you replace it.