Analytical and numerical study is carried out to study the behavior of stick-slip and judder phenomenon during engaging and disengaging of the automotive clutch. For this purpose, a four degree of freedom torsional power train lumped mass model is developed. This torsional vibration system includes engine-flywheel, clutch, gear box and vehicle drive line, which are connected to each other by shafts. Equation of motion of the system is developed and initially a stability analysis is carried out for various gradients of coefficient of friction using eigen value analysis. Later, a numerical simulation is carried out to analyze the judder and stick-slip phenomenon using commercially available mathematical tool MATLAB. It is observed that the clutch stick-slip is increased with increase in external torque and clutch pressure fluctuations.