The aim of this research study was to analyse the approaches for establishing a spatial model of a radial truck tyre, based on the finite element method, in order to perform a realistic analysis of static as well as dynamic tyre–pavement interactions. A complex rubber tyre model having a large number of elements was formulated combining current state-of-the-art modelling techniques and, from that model, a simplified model having a smaller number of elements was derived. The complex model proved to be useful only for static loading, because of its high computational demand, while the simplified model proved to be also suitable for dynamic modelling. The two tyre models having different numbers of elements were compared by analysing the contact areas and stresses. Our results indicate that the basic idea of not changing material characteristics while simplifying the model, rebuilding only the carcass using composite shell elements, did not prove to be a satisfactory direction. The results given by the simplified model do not describe the behaviour of the radial tyre well but, rather, describe the behaviour of the diagonal tyre, regarding contact areas and stresses. On the contrary, when analysing stresses and strains in the road pavement structure, the two finite element models provided similar results in practice. Based on our comparison calculations, applying the average contact pressure $q$ at analysis points at a 5–8 cm depth, the contact behaviour of the finite element tyre model can be used in any elastic-layer theory-based software.