In recent years, automatic transmissions have become widely used in cars. Compared to manual transmissions, automatic transmissions suffer from poor fuel economy. In order to overcome this disadvantage, a lock-up clutch system in the torque converter has been applied. When the rotating speed of the turbine approaches that of the pump, the input shaft is directly connected to the gear train through friction by means of the lock-up clutch. In the process of slipping at the lock-up clutch, frictional vibration referred to as shudder sometimes occurs. When shudder occurs, the power train, as well as the tires and the car seats, vibrates. Therefore, the shudder adversely affects passenger comfort. In the present study, experiments are conducted to analyze the shudder mechanism using a bench test apparatus and an actual vehicle. The characteristics of friction in the lock-up clutch is found to have a negative slope with respect to the relative slip velocity. The entire system from the piston to the tires, including planetary gears, is modeled as a linear multi-degree-of-freedom system using a Lagrange equation of motion, and the shudder mechanism is clarified. A countermeasure for suppressing shudder is also proposed. The most effective position at which to add the viscous damping and the countermeasure to suppress the shudder by attaching a dynamic absorber are analyzed. Numerical analysis reveals that (1) applying dampening to the dampers is the most effective method by which to suppress the shudder and (2) the shudder can be completely suppressed by attaching a dynamic absorber. Moreover, experiments using a dynamic absorber are conducted using an actual vehicle, and the suppressive effect of the dynamic absorber on the shudder is confirmed through experiments.