In this paper we present the main results of an extensive comparison carried out between the most modern theoretical models of stellar structure, including moderate core over- shooting and mass loss, and the best available data of apsidal motion rates for double-lined eclipsing binaries. Though stellar absolute dimensions (radii, temperatures, etc) for the selected sample of binaries compare well with theoretical predictions, the internal structure constants derived from the observed apsidal motions have been reported for long time to denote stellar configurations which are more centrally concentrated in mass than expected from the models. A quantitative assessment of these differences has been made and several possible explanations have been explored. The systematic effect is actually very much decreased when we use the latest opacity tables and take into account the influence of rotation in the stellar models. The opacities recently published by Rogers & Iglesias (1992) have been used throughout in this paper. Uncertainties in the stellar models are briefly discussed in order to assess the reliability of the theoretically predicted stellar dimensions and internal structure constants, and the need to introduce some amount of overshooting in the convective cores of the stars has also been discussed. In order to evaluate the effects of rotation in the internal structure constants, we have computed theoretical models using the Kippenhahn-Thomas formalism which treats distorted configurations as equivalent spheres. Through this exploratory model, we have found that the corrections introduced in the second order apsidal motion constant, log k2, by stellar rotation are well represented by means of a linear expression in terms of the parameter λ, as given by Stothers (1974). A significant correlation has been found between the discrepancies in log k2, derived from the comparison of observed values with non rotating models, and the parameter λ. After correction for this effect, we have found that, for the first time, the systematic deviations between observational and theoretical values of log k2 are not significantly detected. However, it must be pointed out that some evolved systems still show slightly discrepant log k2 values. They are discussed, in a case by case basis, but it should be mentioned that we have found evidences of a correlation between the anomalous systems and the proximity of their components to the Roche critical surface.