Abstarct: Optimum boundaries of two and three-dimensional elastic structures are sought. Weight of structure and stress limitations are considered as objective and constraints of the optimization problem, respectively. There are three types of optimization methods in literature called mathematical, optimality criteria and mextaheuristic baxsed approaches. In this research, the Method of Moving Asymptotes (MMA) which is from mathematical baxsed approaches is utilized to deal with shape optimization problem. Since derivatives of objective and constraints functions are needed in MMA, sensitivity analysis forms part of this research and an analytical approach is developed for this purpose. The IsoGeometric Analysis (IGA) method is employed for structural analysis. In this method unknown function (deformation) is approximated by Non-Uniform Rational B-Splines (NURBS) basis functions which are also used for creating geometry of the structure. Consequently, by changing the position of control points of NURBS, the geometry and the analysis model will change, simultaneously. Therefore, there is no need to regenerate the analysis model during the optimization iterations, which is the case when the Finite Element (FE) method is used as the analysis engine. In order to verify the derived sensitivity equations, demonstrate the ability of MMA in solving shape optimization problems and check the code written in this thesis, several two and three dimensional illustrative examples are presented and the results are compared with other optimization methods, reported in relevant references, such as Sequential Quadratic Programming (SQP) method.