Compliant mechanisms whose dominant modes of vibration match the desired kinematics for locomotion in a given environment are used to mimic motions of a living animal. Mechanisms are simple and mechanically robust. They may have as few as one actuator, which excites the compliant portion to vibrate in a natural mode that results in motion that mimics a living animal. Additional actuators may drive directional elements such as flippers. Models for compliant mechanism bodies were derived and used to identify actuator, material, and geometrical properties of the required mechanisms. The design and fabrication techniques of mechanisms implementing these ideas is also presented. Experiments found that important features of fish-swimming kinematics can be captured qualitatively by compliant mechanisms. The resulting mechanism swimming performance was ⅓ of the real fish performance, comparable to current robotic fish. A compliant mechanism approach to biomimetic locomotion has significant advantages since mechanisms are simpler and more robust than traditional mechanisms used for biomimetic robots and performance achieved is comparable. Radio control is straightforward. The flexible material may be uniform, but need not be. Active materials, such as piezoelectric materials may be used to change the stiffness or other mechanical properties of the flexible portion. The material may be distributed uniformly or non-uniformly. The tail portion may be tapered or uniform or variable cross-section.