The approximate torque response model for the engagement of a wet friction clutch, developed by Berger [1, 2], was modified and enhanced. The modified Reynolds equation for the film thickness and force balance for the wet clutch pack are solved numerically. The Reynolds equation relates the film hydrodynamic pressure to the film thickness, physical properties of friction materials, and operating parameters. The torque is calculated from the film and asperity pressure distribution at the friction interface. The applied pressure and the interface temperature as a function of time during engagement are considered in the model. The correct average flow factors of Patir and Cheng [3, 4] for ATF flow between rough surfaces are incorporated into the model. The permeability of friction materials and the temperature gradient inside the friction material are considered.The key input parameter for predicting the torque response is the friction coefficient as a function of sliding speed, temperature, and pressure, which can be measured by the Low Velocity Friction Apparatus (LVFA). The effects of physical and operating parameters on the torque response are demonstrated. Finally, the model predictions of the torque response are compared favorably with the experimental measurements under various operating conditions.