The dynamic contact mechanics of isotropic elastic coating bonded to homogeneous substrate was examined. The coating is indented by a sliding rigid punch of a cylindrical profile. The rigid punch moves over the coating at a steady subsonic speed. To determine contact stresses, an analytical method based on the singular integral equation technique is put forward. Governing partial differential equations are derived considering general theory of elastodynamics. The influences of dimensionless punch speed, mass density ratio, shear modulus, coefficient of friction, relative coating thickness and Poisson's ratio on contact stresses and contact related parameters were found. Comparison of the contact stresses computed by elastodynamic and elastostatic theories clearly shows that the relative difference between these two results is quite remarkable. Hence, in sliding contact problems incorporating punches with relatively high speed, elastodynamic theory is required to find more realizable stress results.