What you have is an SM318 3 speed trans which is the most common 3 speed trans used by GM in the mid 50's through the mid 60's. They came in the long tailshaft version - about 23" and the short tailshaft - about 15". There is also an overdrive version. The internal parts are the same on all models (except Corvette). Parts should be available through a transmission parts supplier in your area. If not, I can provide you with a supplier that I am familiar with in So Cal. I would double check the reverse idler gear as it could be damaged as well. These transmissions are usually available at most swap meets for a reasonable price. Depending on what other components are worn or damaged, it may be better to look for a replacement.
Fred

Last edited by rfs56trk; 05/13/2010 4:12 PM.

1956 3100 Pickup/Red/350/3sp OD/PS/Disc Brakes
1957 Bel Air Sport Coupe/Red/355/TH350/PS/Disc Brakes
2017 Silverado LT Single Cab SB/Black/5.3/6 Speed Trans
1947 Willys CJ2A w/F-Head engine