In order to reproduce the experimental T c and tunneling data of high- T c superconductors in the framework of the Eliashberg theory for strong electron–boson interaction, it is necessary to use large values of the coupling constant. In this work, we investigate whether this fact is a possible consequence of the breakdown of Migdal's theorem that certainly occurs in the cuprates due to their very low value of Fermi energy as compared to the characteristic phonon energy. In order to numerically quantify the consequences of the violation of the Migdal's approximation, we use the theoretical approach developed by Pietronero et al. [L. Pietronero, S. Strässler, C. Grimaldi, Phys. Rev. B 52, 10516 (1995)] and Grimaldi et al. [C. Grimaldi, L. Pietronero, S. Strässler, Phys. Rev. B 52, 10530 (1995)] on experimental data taken from the literature. The effects on the electron–phonon coupling constant λ, on the critical temperature T c and on the superconducting gap Δ are calculated also by means of a direct solution of the standard Eliashberg equations and discussed in different kinds of superconducting materials both with low and high critical temperature.