Aims. One of the most reliable means of studying the stellar interior is through the apsidal motion in double line eclipsing binary systems since these systems present errors in masses, radii, and effective temperatures of only a few per cent. On the other hand, the theoretical values of the apsidal motion to be compared with the observed values depend on the stellar masses of the components and more strongly on their radii (fifth power). The main objective of this work is to make available grids of evolutionary stellar models that, in addition to the traditional parameters (e.g. age, mass, log g, Teff), also contain the necessary parameters for the theoretical study of apsidal motion and tidal evolution. This information is useful for the study of the apsidal motion in eclipsing binaries and their tidal evolution, and can also be used for the same purpose in exoplanetary systems. Methods. All models were computed using the MESA package. We consider core overshooting for models with masses ≥1.2M⊙. For the amount of core overshooting we adopted a recent relationship for mass × core overshooting. We adopted for the mixing-length parameter αMLT the value 1.84 (the solar-calibrated value). Mass loss was taken into account in two evolutionary phases. The models were followed from the pre-main sequence phase to the white dwarf (WD) stage. Results. The evolutionary models containing age, luminosity, log g, and Teff, as well as the first three harmonics of the internal stellar structure (k2, k3, and k4), the radius of gyration βy, and the dimensionless variable α, related to gravitational potential energy, are presented in 69 tables covering three chemical compositions: [Fe/H] = −0.50, 0.00, and 0.50. Additional models with different input physics are available.