The Volmer-Heyrovsky-Tafel mechanism for the hydrogen evolution reaction in alkaline solutions, using a generalized adsorption model for the reaction intermediate, was solved under steady state conditions without any kinetic approximation. The electrode surface was modeled through a distribution function of the standard Gibbs energy of the adsorbed atomic hydrogen. This is characterized by its property of describing a generalized Freundlich-type adsorption. The dependences of the current density and the surface coverage on the overpotential were evaluated for the Volmer-Heyrovsky and Volmer-Tafel routes, and for the parallel course of these two routes, with different values of the model parameters. The results obtained show that the present model can correlate a great variety of kinetic behavior, and demonstrate the importance of the evaluation of the equilibrium surface coverage and the distribution function of the adsorbed species through alternative methods of kinetic study.