Rail-wheel contact problems have been analyzed by applying three-dimensional finite element models. Based on these models, the applicability of the Hertz contact theory (HCT) to rail-wheel contact problems is verified in the present paper. Beside a standard rail, also a crane rail and a switching component are considered in the verification. In the case of a contact between the standard rail UIC60 and the standard wheel UICORE, different transverse contact positions are analyzed. Numerically calculated distributions of the contact pressure for different types of rails with respect to different initial contact positions agree with the results from the HCT only if either the contact zone does not spread into a region of changed surface curvature or if plastification does not occur. Finally, the convective part of the dissipation power due to friction is calculated, which cannot be provided directly by the HCT.