To put the above answers in context...this question is asked very often and the answer is pretty much always the same. To summarize:
S & W has stated any model stamped steel frame .38 Special revolver is safe for +P use in the past. However, they have no control over what happens to their guns after sale, and my guess is the lawyers have become involved, so if you call them and ask "can my .38 such-and-such use +P?" you will most likely hear that "only revolvers stamped with this rating can use this ammo". It's the safe answer for them, and understandable.
However, standard pressure .38 Special is rated at 18,000 and official +P 21,000 psi. Is this more stress on the gun (and shooter)? Yes. If you put 10,000 rounds through your model 60, will it increase the tolerances on the gun to the point that it may need work? Maybe. Will it make an otherwise mechanically sound steel J frame (or the tank-like SP-101) explode into little metal fragments? No.
Bottom line, your hand (and wallet) will tire of shooting +P .38 before anything will happen to a model 60 in good condition. Hope this is helpful.