The paper addresses finite element formulations for automobile tires considering nonlinear material behavior, large strains, and finite deformations while using efficient computational strategies for realistic large‐scale 3D finite element simulations. A new 3D finite element model for cord‐reinforced rubber composites is employed for the numerical representation of the reinforcing plies. A hyperelastic Mooney material law in conjunction with a hybrid finite element formulation is used for the modeling of the rubber material. A strategy for the generation of locally refined finite element meshes of automobile tires is developed. Several computational strategies, together with an iterative solver, are proposed to improve the computational efficiency. 3D simulations of factional static contact of automobile tires on a rigid road surface, involving the determination of the pressure distribution in the contact zone, are presented.