Introduction.The article represents the mathematical model of commercial vehicle’s hydraulic retarder. The model is based on the mathematical model of the variable filling hydraulic dynamometer.Materials and methods.The retarder model was designed with the possibility of its integration with the mathematical model of the engine cooling system. For this purpose, the state function of fluid temperature in a working chamber of the retarder was added to the retarder model. Consequently, fluid compression in the working chamber was included into the model to avoid unlimited filling because of possible high pressure at the retarder inlet.Results.The simulation model of the retarder was established as LMS Amesim submodel using C-programming language. For testing, the retarder simulation model was integrated with the Amesim models of the engine cooling system and with the powertrain and vehicle movement dynamics. In addition, brake torque regulation wassynthesized on PI controllers.Discussion and conclusions. During simulation of the vehicle movement on the mountain route expectable results were obtain, such as continuous braking via the retarder, which led to increasing of the cooling system’s fluid temperature. Therefore, overfilling of the retarder working chamber didn’t occur through the fluid compression. The retarder model could be applied to determine retarder design influence at vehicle functioning. For instance, it could be used for development of the algorithms’ control.