In this thesis, finite point method (FPM) has been used as a numerical solution tool in topology optimization of structures. The motive is to obtain clear topologies, with smooth interfaces between the black and white zones, by adding new points. To this end, capability of the standard version of FPM in modeling of domains with variable density has been examined. The results show that the method does not produc accurate sensitivities for further use in optimization algorithm. To improve the method, some new versio have been proposed and tested. Among them is a version based on finding the extremum of an appropriate functional in order to derive the required collocation equations. The principle of the method is similar to mixed methods in FEM, i.e. mixed stress-displacement formulations, and likewise some instability effects, due to the type of DOF used at each point, are seen in the solution. In order to eliminate such instability effects, some additional constraints are considered for the variational problem. This has been performed by considering a secondary grid of points, with fewer points than the main one, and writing a set of constraint-like equations between the nodal displacements of the two grids. The method is called “ Constrained Pseudo Variational form of Finite Point Method ”. It appears that the proposed is capable of producing accurate sensitivities. The method has been used in a two dimentional topology optimization problem. To obtain clear topology a power-law method has been employed. The results show that the proposed method is suitable for being used as a solution tool in optimization problems.