This Project focuses on obtaining an approximation solution for solving a system of two dimensional linear Fredholm integral equations of the 2nd kind. Various numerical procedures are reformulated and applied for solving the above system with their newly written computer programs.such as;Numerical integrations methods for multiple integral (composite Simpson s method & composite trapezoid method); four different types of weighted residual methods (collocation method, sub-domain method,least square method and Galerkin method) and two different types of Iterative methods (successive approximation method and Adomian decomposition method).