This work introduces a framework for the creation and analysis of efficient gaits for legged systems based on the exploitation of natural dynamics. It summarizes the theory behind hybrid dynamic modeling, the identification of optimal periodic motions with single shooting and direct collocation, and the analysis of first order stability. Three examples introduce various aspects of gait creation and analysis: a stability study of a passive dynamic walker determines the ideal position of the leg's center of mass, the cost of transportation is minimized for a prismatic monopod hopper based on series elastic actuators, and a basic controller is created for the model of a bounding robot. The presented tools and examples are freely available at www.asl.ethz.ch/people/cremy/personal/GaitCreation. © 2011 IEEE.