Nonadiabatic theory of chemical reactions is applied to the kinetics of the dissociative adsorption of homonuclear diatomic molecules on transition metal surfaces. Coordinates that characterize substrate nuclei vibrations are introduced into the theoretical model to take into account a reorganization of the substrate structure under adsorption process along with those that characterize approaching of an adsorbate molecule X2 to a substrate S and vibration motion of the molecule. The substrate is modeled by a set of the classical harmonic oscillators. An approximate expression for the activation energy is obtained under general assumptions about the form of both intermolecular potentials v1 and vf characterizing the interaction of the adsorbate and substrate, and intramolecular potentials ui and uf characterizing the interaction between X atoms in the initial and final states, respectively. These assumptions allow one to calculate the activation energy in the explicit form without the detailed information about these interaction potentials. In the model, the activation energy to the dissociation is determined by the repulsive interaction of reactants, the substrate reorganization energy, and an effective energy of the reaction.