This thesis is concerned with the development of using finite point method for solving partial differential equations. The traditional mesh-based methods for solving partial differential equations are based on a mesh generation which is a complicated and time consuming process especially for complex geometries. One of the mesh less methods is the finite point method (FPM) introduced by Onate et al. (1995) who directly collocated the moving least squares (MLS) approximation for the approximate solutions of partial differential equations. The finite point method is very simple to implement because it is a truly mesh less method in the sense of that no connectivity information is required for the set of collocation points. One limitation of the mesh less methods found in the literature is that few of them have a rich mathematical background to justify their use. That is mathematical proofs of sufficient conditions to guarantee that these methods will converge to the true solution which is not available. The error estimates for the finite point method in Sobolov spaces in multiple dimensions when nodes and shape functions satisfy in certain conditions have been investigated by Cheng et al. (2008). An important objective of the present research is to develop the finite point method for complex geometries and computationally efficient procedures for use in large scale problems. The structure of this thesis is as follows. In chapter one, we review some definitions and theorems which will be used in the next chapters. In chapter two we have investigated some researches about moving least squares approximation and the finite point method. The error analysis of the finite point method is investigated in this chapter too. These results are tested in chapter three with some numerical examples. Moreover in this chapter, the finite point method is proposed for solving the p-Laplace equation in complex domains. In chapter four the finite point method is implemented for parabolic equations. A novel method is applied to demonstrate the stability of the finite point method for solving time-dependent partial differential equations in this chapter. Also performance of the stabilized finite point method is shown for convection-diffusion equations with large Peclet numbers. Finally in chapter five a kind of finite point method in finite difference mode is represented for solving large scale problems and particularly for sine-Gordon equation.