The contact of coated systems under sliding conditions is considered within the framework of elasticity theory with the assumption of perfect bond between coating and substrate. Formulation is introduced in the form of a system of coupled singular integral equations of the second kind with Cauchy kernels that describe contact problems for coated bodies under complete, semi-complete and incomplete contact conditions. Accurate and efficient numerical method for the solution of sliding contact problems is described. Explicit results are presented for the interpolative Gauss-Jacobi numerical integration scheme for singular integral equations of the second kind with Cauchy kernels. The method captures correctly both regular and singular behavior of the traction distribution near the edges of contact. Several cases of sliding contact are considered to demonstrate the validity of the method.