An efficient approach for generating pin-jointed compliant mechanisms is presented. A compliant mechanism uses the elastic deformation of structural parts to realize the mechanism for shape transformation of the entire structure, which is contrary to the conventional link mechanism. Ohsaki and Nishiwaki (Struct. Multidisc. Optim., Vol.30, pp.327-334, 2005) presented a method for generating flexible multistable bar-joint mechanisms using nonlinear programming approach. However, due to highly nonlinear property of the problem, the nonlinear programming problem should be solved many times with random initial solutions to obtain several types of mechanisms. Since the compliant pin-jointed mechanism is usually statically determinate, the optimization problem can be solved easily if the design space is limited to statically determinate structures. Avis et al. (Proc. of COCOON 2006, LNCS 4112, pp.205-215, 2006) presented an algorithm for enumerating all the non-crossing generically minimally rigid bar-joint frameworks, which are regarded as statically determinate trusses in structural engineering. In this paper, bistable mechanisms utilizing snapthrough behavior are obtained more efficiently with the algorithm. In the numerical example, many types of bistable compliant mechanisms are generated.