The paper describes the authors' contribution to the evolution of numerical simulation of concrete structures based on the nonlinear finite element method. The formulation of constitutive relations for concrete material is a keystone of this approach, whereas cracking is the dominant feature. Two distinct methods of crack modeling were developed, namely, the discrete and the smeared crack models. Blind prediction benchmarks of the experimental tests are used for model verification. Application of the numerical simulation in the design of concrete structures is supported by the global safety format, where the uncertainty sources, due to the material and the resistance model, are considered. A structural assessment of a prestressed reinforced concrete viaduct is shown as an example of application.