The problem of pulling the reinforcing bar from the concrete block is urgent for the practice, as it represents the most widespread method of experimental evaluation of characteristics of reinforcedconcrete bond behavior, which are necessary for an estimation of the strength and durability of reinforced concrete structures. Fracture process of bonds at pulling the rebar from the concrete is a complex multistep process, accompanied by the presence of inhomogeneous and inelastic deformation, a 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 problem of pulling the reinforcing bar from the concrete block have been obtained with using various models of bond behavior and concrete cracking. The comparison of obtained numerical results with 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, while the second part is concerned with the models without explicitly taking into account of discontinuities.