A plane contact and partial slip model of an elastic layer with randomly rough surface were established by combining the Greenwood–Williamson (GW) rough contact model and the Cattaneo–Mindlin partial slip model. The rough surface of the elastic layer bonded to a rigid base is modeled as an ensemble of noninteracting asperities with identical radius of curvature and Gaussian-distributed heights. By employing the Hertzian solution and the Cattaneo–Mindlin solution to each individual asperity of the rough surface, we derive the total normal force, the real contact area, and the total tangential force for the rough surface, respectively, and then examine the normal contact and partial slip behaviors of the layer. An effective Coulomb coefficient is defined to account for interfacial friction properties. Furthermore, a typical stick–slip transition for the rough surface was also captured by distinguishing the stick and slip contacting asperities according to their respective indentation depths. Our analysis results show that an increasing layer thickness may result in a larger real contact area, a lower mean contact pressure, and a higher effective Coulomb coefficient.