In order to improve the accuracy of the strength assessment of operating reinforced concrete structures, it is rational to use the model with a discrete location of reinforcing bars with the actual characteristics of adhesion to concrete reinforcement. The problem of pulling the reinforcing bar from the concrete block is relevant for the practice, as it represents the most widespread method of experimental evaluation of characteristics of reinforced-concrete bond behavior. Fracture of bond during the pulling of rebar from concrete is a complex multistep process, characterized with the presence of inhomogeneous and inelastic deformation, the rupture of adhesive bonds, the initiation and propagation of cracks of different shape and orientation, the presence of contact and tribological phenomena. The nonlinear finite-element solutions of the pulling the reinforcing bar from the concrete block problem have been obtained by using various models of bond behavior and concrete cracking. The comparison between the obtained numerical results and experimental data has been presented and discussed. The first part of the article is devoted to the models taking into account the discontinuity of the connection. The second part is concerned with the models without explicitly taking into account discontinuities.