In this study, a numerical solution of elasticity problem is examined. This problem is a plane contact problem. The frictional contact problem for an elastic strip under a rigid punch system is considered. The frictional contact problem is related to infinite length elastic strip in contact with N punches under the influence of horizontal and vertical forces. The lower boundary of the strip is hinged. The solution of contact problems is often reduced to the solution of an integral equation. This integral equation system can be derived from contact problem by using the basic equations of elasticity theory and the given boundary conditions. The singular integral equation system is solved with the help of Gauss Jacobi Quadrature Collocation Method. The frictional contact problem for a homogenous and orthotropic elastic layer are investigated numerically the pressure distribution under the punch system due to the geometrical and mechanical properties of elastic layer are examined and the results are shown in the graphics and tabular form.