Abstarct: In this thesis, the nonlinear stochastic wave equation is solved using the method of radial basis functions. First, we apply the stochastic wave equation to spatial discretization using interpolation of the radial basis functions and use the time integrator method for the temporal discretization of the equation to introduce an explicit iterative method for the numerical solution of the stochastic wave equation. The introduced repetitive method is examined by providing some examples. Also, the stochastic elliptic equation is solved using the element free Galerkin method baxsed on the interpolating moving least squares. First, Galerkin's weak form of the stochastic elliptic equation is formed and the shape functions of the interpolating moving least squares are used. We perform the error analysis of the proposed method and check the error analysis by providing some examples. Finally, we introduce a new idea for applying essential boundary conditions in the element free Galerkin method and examine its error analysis with some examples. In this new idea, the essential boundary conditions are applied to the moving least squares approximation, and then the resulting approximation is used in the element free Galerkin method.