Abstract. In this paper, a straightforward and accurate numerical modeling (a rational function called "tri-root bistable function") are proposed to represent the complete nonlinear bistable force-displacement characteristics. The rational function has a cubic polynomial numerator and quadratic polynomial denominator. With three different kinds of compliant bistable mechanisms, the tri-root bistable function is proved effective and accurate, and that it is capable of capturing the key features of a bistable kinetostatic curve accurately with fewer parameters. Then, for the classic fully-compliant bistable mechanism, six closed-form equations are presented and used to describe the relationships between the tri-root bistable function parameters and the mechanism's design parameters, which are achieved using a multi-variable nonlinear regression. The regression analysis is validated by nonlinear finite element analysis. Finally, a fully-compliant statically balanced mechanism consisting of three different classic fully-compliant bistable mechanisms is illustrated to show the capability of the proposed method in designing compliant multi-stable mechanisms.