A compliant mechanism gains its motion from the deflection of flexible members or the deformation of one portion of materials with respect to other portions. Design and operation of compliant mechanisms are very important, as most of the natural objects are made of compliant materials mixed with rigid materials, such as the bird wings. The most serious problem with compliant mechanisms is their fatigue problem due to repeating deformation of materials in compliant mechanisms. This thesis presents a study on the computational framework for designing a compliant mechanism under fatigue strength control. The framework is based on the topology optimization technique especially ground structure approach (GSA) together with the Genetic Algorithm (GA) technique. The study presented in this thesis has led to the following conclusions: (1) It is feasible to incorporate fatigue strength control especially the stress-life method in the computational framework based on the GSA for designing compliant mechanisms and (2) The computer program can well implement the computational framework along with the general optimization model and the GA to solve the model. There are two main contributions resulting from this thesis: First one is provision of a computational model to design compliant mechanisms under fatigue strength control. This model also results in a minimum number of elements of the compliant mechanism in design, which means the least weight of mechanisms and least amount of materials. Second one is an experiment for the feasibility of implementing the model in the MATLAB environment which is widely used for engineering computation, which implies a wide applicability of the design system developed in this thesis.