The article presents a new contact model of an angular bearing, called the extended model. The model takes account of the effects of centrifugal load caused by thr rotating ring of the bearing and the issue of elasticity. Present models, encountered in literature and referred to in the article as classical, consider the centrifugal force caused by the rotating ball only. Results of analytical research on the extended model and of FEM simulation show explicitly that the contact angles of bearings, and thus contact loads, differ very much from those values obtained in the classical model. These differences are disadvantageous for designing bearing assemblies, since contact loads are greater than those obtained in the classical model. This means, among others, that the present structures with angular contact bearings are in reality subject to greater loads than the constructor has envisaged. The motto of the article is to design analytical calculation models in such a form which would enable the constructor to estimate contact loads, just using a standard scientific calculator or MS Excel type applications; so that there would be no need for solving complex models using numerical methods.