This thesis shows an approach to combine the advantages of MBS tyre models and FEM models for the use in full vehicle simulations. The procedure proposed in this thesis aims to describe a nonlinear structure with a Finite Element approach combined with nonlinear model reduction methods. Unlike most model reduction methods - as the frequently used Craig-Bampton approach - the method of Proper Orthogonal Decomposition (POD) offers a projection basis suitable for nonlinear models. For the linear wave equation, the POD method is studied comparing two different choices of snapshot sets. Set 1 consists of deformation snapshots, and set 2 additionally contains velocities and accelerations. An error analysis proves no convergence guarantee for deformations only. For inclusion of derivatives it yields an error bound diminishing for small time steps. The numerical results show a better behaviour for the derivative snapshot method, as long as the sum of the left-over eigenvalues is significant. For the reduction of nonlinear systems - especially when using commercial software - it is necessary to decouple the reduced surrogate system from the full model. To achieve this, a lookup table approach is presented. It makes use of the preceding computation step with the full model necessary to set up the POD basis (training step). The nonlinear term of inner forces and the stiffness matrix are output and stored in a lookup table for the reduced system. Numerical examples include a nonlinear string in Matlab and an airspring computed in Abaqus. Both examples show that effort reductions of two orders of magnitude are possible within a reasonable error tolerance. The lookup approaches perform faster than the Trajectory Piecewise Linear (TPWL) method and produce comparable errors. Furthermore, the Abaqus example shows the influence of training excitation on the quality of the reduced model.