In the paper has been theoretically analyzed the influence of the nano-sized defects created in HTc superconductors, for instance during the irradiation in the nuclear accelerators, on the current-voltage characteristics and critical current of the HTc superconducting tapes, subjected to the bending strain process. Theoretical model of these characteristics has been proposed basing on the analysis of interaction of the magnetic pancake type vortices with nano-sized defects for various initial states. The model of the change of the bending strain acting on the superconducting filament or film for the second generation composite tape, in the comparison to the applied bending strain, following from the elasticity properties of superconducting tape and geometrical factor has been presented. Current-voltage characteristics versus bending strain have been calculated, which results are in good agreement with experimental data measured on Bi-2223 tape at liquid nitrogen temperature. Model predicts too the appearance of the dynamical anomalies of the current-voltage characteristics, observed us previously.