A simplified three-degree-of-freedom dynamic model with nonlinear friction torque and engine torque excitation, capable of identifying the effect of the engine excitation on clutch judder, is presented. The analysis of harmonic order is performed and a sinusoidal contact pressure between friction surfaces is considered, along with an analytical solution for the relative angular velocity of the clutch plates. The average fluctuation amplitude of the clutch relative angular velocity is used to evaluate the judder. Numerical calculations indicate that the clutch judder increases significantly when the angular velocity of the crankshaft, corresponding to the harmonic orders of the engine, is equal or close to the natural frequency of the driveline. An identical frequency of the engine excitation and the oil pressure fluctuation contributes little to the clutch judder, unless the excitation is at or near the resonance frequency. The amplitudes of oscillations due to the engine excitation grow when the pulsating torque of the engine increases. The mean torque of the engine has little influence on the judder, although it governs the clutch engagement time. The results further show that clutch judder attenuates as the torsional stiffness of the system increases.