The paper presents a model of the sealing process in kinematic pairs of hydraulic cylinders with elastic seals and an analytical form of this model based on the results obtained by the author. The prepared model distinguishes rheological parameters, allowing one to determine the criteria of a correct course of the sealing process and to forecast the operating time for the seals. Exemplary test results and their analysis are presented, too. It results from the analysis that leakage efficiency through the seal is dependent on the sealing pressure determined by the parameter 8, and it is unstable in relation to this parameter. Basing on this fact, the author determined conditions of hydrodynamic convection of the sealing and elaborated an analytical model of the sealing process including roughness of the piston rod surface as well as the seal flexibility.