In this chapter, the tire-pavement system as one subsystem of the complex vehicle-tire-pavement system is investigated in detail. As basic framework, the finite element method (FEM) is used for both, tire and pavement simulation, to obtain a detailed representation of the dynamic system, where the special case of steady state motion of the rolling tire is considered. The finite element (FE) discretization further enables to study the tire-pavement interface in terms of transmitted stresses and friction characteristics for different tire and surface properties. For the modeling of this complex subsystem, new FE based analysis methods have been derived using the Arbitrary Lagrangian-Eulerian (ALE) framework for tire and pavement. With the help of the ALE framework, the relative motion of tire and pavement is captured in a computationally efficient way. Friction in the tire-pavement interface is numerically represented by a homogenization approach of the friction interface over several length scales. With the help of a time homogenization technique, spatially detailed long-term predictions regarding rutting of the pavement become feasible by considering different time scales of the thermo-mechanical investigation.