Bistable mechanisms, which have two stable equilibria within their range of motion, are important parts of a wide variety of systems, such as closures, valves, switches, and clasps. Compliant bistable mechanisms present design challenges because the mechanism’s energy storage and motion characteristics are strongly coupled and must be considered simultaneously. This paper studies compliant bistable mechanisms which may be modeled as four-link mechanisms with a torsional spring at one joint. Theory is developed to predict compliant and rigid-body mechanism configurations which guarantee bistable behavior. With this knowledge, designers can largely uncouple the motion and energy storage requirements of a bistable mechanism design problem. Examples demonstrate the power of the theory in bistable mechanism design.