The optimized design of a large variety of rubber-made engineering applications (e.g. tires, dampers, rubber seals) needs the full solution of many mechanical problems involving viscoelasticity. Particularly interesting is the sliding contact mechanics of rough viscoelastic solids, where, in addition to the convoluted nature of the material response, the surface roughness boosts the problem complexity. In this paper, by employing the adaptive non uniform mesh developed by the authors in [1, 2] and the mathematical formulation proposed in [3], we focus on the main aspects of this issue, i.e. the viscoelastic dissipative phenomena and the viscoelastic induced anisotropy.