One presents a mathematical method to study the elastic deformations of mechanical face seal rings under the action of temperatures, pressures and centrifugal forces, the only able to offer information on its deformations, which appear only in running of a mechanical face seal. The obtained results are very important taking into consideration the value of micron order of the clearance between the two rings and give a theoretical explanation of the negative influence of its varied working regime. The method permit the increase of mechanical face seal reliability by the study of the influence of geometry and the materials of two rings in contact with the fluid film with different hydrodynamic properties.