Being one of the most challenging tasks in structural designs, topology optimization seeks a suitable layout of structures for the required structural performance. In this regard, various techniques and methods have been developed during the past decade. The choice of theory and methodology of the structural analysi plays a crucial role in the design. Recently, a number of mesh-free methods have been proposed to alleviate some drawbacks of mesh-based approaches. In this dissertation, the procedure of topology optimization of continuum structures is combined with some mesh-free approaches. In this regard, at first, a mesh-free method known as Generalized Finite Point Method (GFPM) is used to perform structural response analysis as well as the sensitivity analysis. This method employs a weighted residual approach and is based on a sub-domain collocation technique. The shape functions are constructed by the weighted least square (WLS), and the system of algebraic equations is constructed by the use of weak form of the generic governing equation of elasticity problem. Due to the use of weak form of equations, the method can consider density variation, which is an important requirement in topology optimization, but the results show that GFPM does not perform accurate sensitivity analysis when used in optimization algorithm. To improve the method and eliminate some instability effects, two new mesh-less methods have been proposed and employed in topology optimization procedure which are called “Petrov-Galerkin Free Patch Method” and “Free Patch Method”. These methods are based on employing finite element shape functions as basis functions to approximate displacement field and using the weak form of the governing equations. Unlike the other integral-based mesh-free methods, the computation of the related integrals is significantly simple and cheap, so the proposed methods will save the time and cost of analysis. A density approach is employed to find the optimal material distribution in a continuum domain. The density at a generic point is evaluated by interpolation between a set of nodal values which are independent from those used for the analysis. To interpolate the density value from nodal quantities, a set of linear hat-shape functions are defined over elements that have been used for discritization of the material field. To obtain the optimum configuration, a restriction method is employed which is based on a sequential mesh refinement strategy during the optimization procedure. Moreover, The optimization problem is solved by using the Method of Moving Asymptotes (MMA) where the objective function is the compliance energy and nodal densities are used as design variables. The solutions of several 2D structural optimization problems with various boundary conditions are presented to validate the accuracy, efficiency and applicability of the proposed methods. It has been observed that the presented methods prevent some numerical instabilities such as appearance of checkerboard patterns and mesh-dependence phenomena. Key words : Topology Optimization, Mesh-free Methods, Numerical Instability