Hydraulic retarders are auxiliary braking devices that reduce the velocity of a vehicle, particularly when a vehicle is driven downhill. Such velocity reduction could reduce the potential risk caused by brake failure caused by the service brake working for a long time and the temperature of the brake shoe becomes extremely high. This paper introduces the construction of the hydraulic retarder and proposes two mathematical models for the hydraulic retarder. The first mathematical model is deduced by using fluid mechanics, which is used to analyze the mechanism of how braking torque is produced and the key factors that can influence the value of the braking torque. The second mathematical model is deduced by using thermodynamics, which is used to quantify the heat produced by the hydraulic retarder. This research emphasizes that the flow rate and the average velocity of the working fluid in the working chamber mainly determine the braking torque of the hydraulic retarder. The flow rate into and out of the working chamber determines the temperature rise of the working fluid. Computational fluid dynamics (CFD) simulations are conducted with the Reynolds-averaged Navier-Stokes (RANS) and Shear Stress Transport (SST) turbulent models. Experiments are carried out to justify the two mathematical models and the CFD simulations. The results show that the mathematical models are capable of describing the force analysis and energy conversion of the hydraulic retarder and SST is more accurate for CFD simulation and the error is within 6 %.