The direct finite element modeling of deformation and fracture processes in the concrete matrix of the road bridge under the operating loads and the reinforcement corrosion has been performed with account of damage accumulation in concrete. The obtained results of nonlinear boundary value problems in three-dimensional formulation for a representative volume of the lateral part of the bridge show an agreement with the failure character observed in reality. The proposed approach allows identifying potential mechanisms of cracking of reinforced concrete structure at the design stage and analyzing the durability of such structures subjected to corrosion of steel reinforcement. This approach also allows estimating the residual life of partially damaged structure with account of prehistory of its use. However, the practical implementation of this approach requires the large computational effort and additional experimental data on changes in the mechanical properties of concrete due to aggressive environmental influences.