Introduction. Methods of energy saving in pneumatic drive are considered. The method of braking by creating back pressure in the exhaust cavity of the pneumatic actuator is of interest. Under braking, the compressed air energy is stored in the recuperative volume. It is possible to control the braking dynamics through setting the initial parameters of the recuperative volume. The work objective is to create a mathematical model describing the dynamic processes taking place in the pneumatic drive under braking by backpressure, with a constant mass enclosed in the cavities of the air motor, and considering variation of the initial parameters of the braking volume.Materials and Methods. A mathematical model is proposed that describes the speed change of the output link, pressures and temperatures in the cavities of the pneumatic drive depending on the initial parameters of the recuperative volume. The solution to the mathematical model is carried out by the numerical integration method.Research Results. The dependences of the output link velocity, pressures and temperatures in the pneumatic drive cavities on the initial parameters of the recuperative volume are obtained. Adequacy of the built mathematical model is confirmed by Fisher's criterion.Discussions and Conclusions. The results obtained can be used to solve the problems of energy saving in pneumatic drives under the organization of backpressure braking. The use of recuperative volume increases the technological flexibility of the drive during its readjustment and extends the possibilities of energy saving.