This paper presents a detailed investigation of the dry clutch engagement process, and vehicle start-up judder phenomenon that could result in the deterioration of vehicle ride comfort. Elasto-plastic friction model is elaborated through the slider-pulley system, which shows some friction characteristics such as presliding, stick-slip motion, Stribeck effects, etc., and applied to dry clutch. The axial compression characteristics of three elastic parts, which include diaphragm spring, cushion spring, and link strip have been taken into consideration, and nonlinear relationship between the release bearing travel and the clutch clamp force is also established. The powertrain system model of front-engine and front-wheel-drive vehicle equipped with manual transmission is set up to recreate the start-up judder phenomenon in the numerical simulation and analyze its mechanism. The sudden transfer of the engine torque during the clutch engagement process results in the initial judder, which can be supposed as the step response of system and is initially weakened due to the damping of the powertrain system. Then the judder gradually strengthens and gets in the most severe vibrance when the clutch is about to get in to the fully engaged state, which is related to the frictional characteristics that forms a closed-loop positive feedback system, as well as the frequent state transitions between sliding state and engaged state. The positive slope of Stribeck effect as well as the reduction of absolute value of negative slope can both effectively suppress the start-up judder, and the apparent judder occurs only if the negative slope is outside of a certain range, instead of in all of the range. In addition, the fluctuation of clutch clamp force can aggravate the start-up judder, in which a more chaotic oscillation is emerged.