The article considers a hydraulic drive designed for the fan transmission, which implements the amphibious vehicle chassis on an air cushion. A mathematical model of the dynamics of the hydraulic rotary drive power section with volumetric regulation has been developed. It is proposed to carry out volumetric regulation by means of a directed change in the working volume of the pump. The dynamics of the output link of the hydraulic drive is calculated when a control signal is applied to change the pump washer angle of inclination. The control signal varied from zero to a signal corresponding to 70% of the maximum, and in the range of 70...100%. The basic and structural diagrams of the hydraulic drive are given; its transient characteristics are obtained when the moment of inertia on the shaft of the hydraulic motor changes when the amphibious vehicle is moving. The simulation study focuses on the change in the moment of inertia on the hydraulic motor shaft under various modes of amphibious vehicle movement. The computational studies of the hydraulic drive determine the time of the transient process and the dynamic error. Computational studies of the hydraulic drive revealed its sufficient performance. The use of the developed mathematical model allows choosing the optimal ratio of the hydraulic drive parameters for an amphibious vehicle.