The design of bistable arches is challenging due to their inherent nonlinear behaviour.It is known that the arch profiles of bistable arches in their two force-free equilibrium states are related to each other through a bilateral relationship.The closed-form analytical form of the bilateral relationship helps in designing the as-fabricated profile of the bistable arches when their toggled shape is completely specified.However, in certain cases, the arch profiles cannot be designed solely using the bilateral relationship.In this paper, we address such cases and present a design method to obtain arch-profiles using shape optimization in conjunction with the bilateral relationship.Such cases include: (1) arch-profiles that are partially specified in the first or/and second states; (2) arch-profiles that extremise the travel have a prescribed change in slope and have a specific ratio of travel between stable and unstable states.Towards this, the arch-profiles are represented using a set of finite variables corresponding to the mode weights of the basis set in which their shape is described.We formulate the optimization problem for each design case with the constraint to restrict the solutions in design space where the arches are bistable.After describing the procedure for numerically solving the optimization problem, design of arch-profiles using this method is illustrated through examples. © 2023, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.