Hmmm. This isn't going to be an easy answer because two things can vary a lot:
1. The structure of the bone
2. The direction of the force

Bones are made up mostly of protein and minerals (calcium and others). When we're born, there's very little mineral. Our bones are soft, flexible cartilage. These bones don't break very easily because they bend so well. They don't allow you to be very strong though, since the force of your muscles just causes bone bending instead of moving whatever you're trying to move. (To see what mineral-free bones are like, put a wishbone in vinegar for a while.) So to get strong, we need more rigid bones. The rigidity also makes bones easier to break. If we use our muscles, our bones get stronger too. They are always being broken down and built up a little at a time. As we get older, we lose bone mass, particularly if we don't get enough calcium or we smoke or drink. This makes bones really brittle because we lack both flexible cartilage and sturdy bone. Men also have denser bones than women of the same size.

The direction of the force makes a difference too. Find a bone picture or model and look at the long bones of the arms and legs. Notice that they're not straight? the bends and shapes make bones better able to take the stress that they normally are subjected to. They are often very resistant to force in one direction, but vulnerable to it in another.

Want to see how the damage for a given force varies with the direction? Get small wooden dowels of the same dimension and subject them to the same force applied in different ways (for example, drop the same weight on the end of one dowel and the middle of another). Use eye protection and other safety measures.

Want to see pictures of a fracture, a weird type of splint, and healing bone? Go to: http://www.eatonhand.com/IMG/img00019.htm DO NOT got to this site if you're easily grossed out!

Materials are often characterized by the ultimate strength which is the stress or pressure required to cause fracture or breakage.This stress can be caused by compression, tension, or shear. The answer for the strength of bone can probably be found in any
physics textbook (it's a pretty popular subject). One number I found for tensile strength is 130 X 10^6 newtons per square meter. This might be in unfamiliar units though. What is this value in terms of psi or atmospheres?

That depends on the bone. It is very easy to fracture a small bone, especially if the pressure is applied across the weakest point. I'm not sure exactly how much pressure is needed, but I can tell you that as little as 25 pounds of pressure applied to one of your small bones will cause a fracture.