A numerical method is developed for solving two dimensional lid driven cavity flows. The finite difference method is used to solve the partial differential equations of two dimensional fluid flow problems .For the sake of simplicity a rectangular solution domain is discussed and the fluid is assumed to be laminar, incompressible, homogeneous, and Newtonian, with uniform fluid properties. The proposed numerical method is used to approximate the values of the variables at the grid (mesh) points, given the boundary conditions. The choice of governing equations whose solutions are sought and the implementation of finite difference methods for the flow conditions with the above specified assumptions are discussed. The implementation methods for the solutions of the variables in the flow have been studied. Graphical solutions have been done by using matlab code.