At present, steam jet vacuum pumps are widely used in various fields of science and technology due to a number of advantages, e.g., reliability, relative simplicity of design, and manufacturability, over other pumping means. The paper analyzes the existing mathematical models of working processes, methods for calculating the pumping parameters of steam-jet vacuum pumps. The problem of improving these methods, which are used in the design, is still urgent. The study attempts to further develop the models in order to increase their practical significance for the pumps design: in particular, the processes of pumping by the first stages of a diffusion pump are considered, since it is they that determine the efficiency of the pump as a whole. Analytical dependences for calculating the main pumping parameters of widely used diffusion vacuum pumps are presented. The obtained equations are a certain clarifying correction of the known provisions on this topic. Findings of research are of practical importance for the design of modern steam-jet vacuum pumps