The article presents a mathematical model describing the operation of a piston pneumatic air engine. Compressed air engines are an alternative to classic combustion solutions as they do not directly emit toxic exhaust components. In the study, a modified internal combustion piston engine was adopted as pneumatic engine. The mathematical model was divided on the two subsystems, that is, mechanical and pneumatic. The mechanical subsystem describes a transformation of compressed air supply process parameters to energy transferred to the piston and further the conversion of the translational to rotary motion; in turn, in the pneumatic part, the lumped elements method was used. Calculations were carried out using the Matlab-Simulink software, resulting in the characteristics of external and economic indicators. The presented mathematical model can be ultimately developed with additional elements, such as the intake or exhaust system, as well as timing system control.