For most animals, locomotion is essential for survival, and it is advantageous to do this efficiently and with minimal neural control. Research has shown that efficient walking is possible without control, resulting purely from the mechanical design of the walker. It is understood that in running gaits, elasticity of muscles and tendons plays a role in preservation of energy.We first describe a rigid body physics engine that is designed specifically for simulating skeletal locomotion. This engine is then used to reproduce canine locomotion in two separate approaches.The first approach is to reproduce the gait of a real dog, as recorded using motion capture. Control is based on local quadratic minimization, and various techniques are used for stability, balance and steering.The second approach is to simulate efficient hoppers, including a two legged alternating hopper that is based on the anatomy of a dog. This hopper has minimal energy loss during ground collisions, and is controlled by changing muscle contractions when they are slack.