The purpose of the article is to provide a mathematical model for the automated pressure selector (APS) designed on the basis of a deadweight pressure gauge tester as a measuring basis of an automated deadweight pressure system for quality control of absolute pressure sensors. The research uses the methods of automated control theory, system modeling, and the basic principles and postulates of gas dynamics. The results of theoretical research of airflow processes with continuous pressure differentials through the throttling sections of the automated pressure selector are presented in the mathematical model. The main parameters of gas dynamic processes occurring in a closed volume where the absolute air pressure is set are determined. It is found that the value of the set absolute pressure mainly depends on the design characteristics of the APS, i.e., on the parameters of the free piston, which performs the functions of both a regulating and sensing element of the automatic pressure control system within the APS. This allowed to implement the fundamental principle of pressure measurement in the automated pressure selector. Considering the results of the theoretical researches of airflow issues and APS design features, a mathematical model of the automated pressure selector has been developed allowing to describe dynamic processes occurring in closed volumes with the precision required for designing of automated control systems. The proposed mathematical model is reduced for calculations and can be used for designing of automated deadweight pressure system for quality control of absolute pressure sensors where modern control methods can be implemented.