Abstract. We propose a structural optimisation method, based on the level set method and using mathematical programming such as the method of moving asymptotes (MMA), which we apply to the design of compliant mechanisms. A compliant mechanism is a monolithic joint-free mechanism designed to be flexible to obtain a specified motion. In the design of compliant mechanisms, several requirements such as the direction of the deformation and stress concentrations must be considered to obtain the specified mechanical function. Topology optimisation, the most flexible type of structural optimisation, has been successfully used as a design optimisation method for compliant mechanisms, but the utility of topology optimisation results is often spoiled by a plethora of impractical designs such as structures containing grayscale areas. Level set-based topology optimisation methods are immune to the problem of grayscales since the boundaries of the optimal configuration are implicitly represented using the level set function. The proposed method updates the level set function using mathematical programming to facilitate the treatment of constraint functionals. To verify its capability, we apply our method to compliant mechanism design problems that include displacement constraints and stress constraints.