In this study, the frictional contact problem of a half plane which has monoclinic material property is considered in the framework of linear elasticity theory. The monoclinic half plane is pressed by a rigid cylindrical punch that transmits both normal and tangential loads. The general expressions of the stress and displacement are determined with using integral transform technique. Utilizing the boundary conditions of the problem, a second kind singular integral equation, in which the unknowns are the contact stress and the contact width is obtained. The singular integral equation is solved numerically using the Gauss-Jacobi integration formulas and the effect of the fiber angle, the friction coefficient, the punch radius, material type and the external load on the contact stress and in-plane stress are given. The analytical solution is compared with the finite element solution and good agreement is obtained.