Everyday, we interact with screens, sensors, and many other devices through contact with the skin. Experimental efforts have increased our knowledge of skin tribology but are challenged by the fact that skin has a complex structure, undergoes finite deformations, has nonlinear material response, has properties that vary with anatomical location, age, sex and environmental conditions. Computational models are powerful tools to dissect the individual contribution of these variables to the overall frictional response. Here we present a three-dimensional high-fidelity multi-layer skin computational model including a detailed surface topography or skin microrelief. Four variables are explored: local coefficient of friction (COF), indenter size, mechanical properties of the stratum corneum, and displacement direction. The results indicate that the global COF depends nonlinearly on the local COF, implying a role for skin deformation on the friction response. The global COF is also influenced by the ratio of the indenter size to the microrelief features, with larger indenters smoothing out the role of skin topography. Changes in stiffness of the uppermost layer of skin associated with humidity have a substantial effect on both the contact area and the reaction forces, but the overall changes in the COF are small. Finally, for the microrelief tested, the response can be considered isotropic. We anticipate that this model and results will enable the design of materials and devices for a desired interaction against skin.