The article describes software developed for simulating mechanical model of a training machine. The training machine is an exosuit with mobile fixing points of feet in stirrups. The exosuit includes four absolutely rigid links to which the feet, the shins, the hips, and the corps of the rider are attached. The foot attachment point corresponds to the horse's center of mass with which the rider interacts by standing in stirrups. The motion of this point is implemented by a telescopic link firmly fixed to a supporting surface. Cylindrical hinges implement rotation of the links. It is assumed that friction in the hinges is negligible. A torque, applied to the hinge that is fixed to the supporting surface, and a lengthwise force, applied to the variable-length link section and thus changing the distance between the link ends, control the telescopic variablelength link that simulate the motion of the horse corpse. The method of programmed motion control is used in the created mathematical model. The developed software is used for synthesizing the exosuit motions close to those of a real horse rider by specifying periodic differentiable functions implementing anthropomorphic motions that subsequently can be used for inverse dynamics problem solution. The exosuit simulation results, obtained using the developed software, can be recommended for designing programmed training machines. These training machines have broad application perspectives not only in sports, but also in medical rehabilitation centers, where they can be used to restore motor capabilities of human musculoskeletal system.