At present peristaltic pumps are widely used in many branches of industry and national economy. Simplicity of construction, processability and possibility of pumping liquids with big quantity of solid particles are the main advantages while using peristaltic pumps. Therefore development of methods of rational choice of parameters at designing of peristaltic pumps is the actual problem. To develop universal mathematical models of dynamic processes in peristaltic pumps for definition of rational technical parameters. In dynamic processes we propose to use differential equations of motion in the Lagrange form, where the angle of rotation of the pump rotor is taken as a universal coordinate. Mathematical model of dynamic processes in peristaltic pump with hydraulic drive has been created on the base of differential equation. The function of resistance forces caused by gravity forces of mixture particles in the hose reel has been determined. On the basis of the non-linear model of the resistance forces to the flow of the fluid Bingham method of constructing the dependence of the pressure drop on the angular velocity of the rotor to determine the resistance forces to the flow of the fluid has been proposed. The result of dynamic processes simulation is the determination of interrelationship of technological parameters of the device functioning: the velocity of the medium and pump performance is increasing at reducing the length of the diverting hose and reducing the height of its rise; a significant influence on the average speed has plastic viscosity of the environment; a significant change in the yield strength has an insignificant impact on the speed.