In a passenger car automatic transmission, the gear ratio is determined by the combination of clutches and brakes, and each element of th planetary gear set is rotated or held stationary by the action of them. In this study, to investigate the shift characteristics of automatic transmission, the equations of motion are derived from the dynamic model of Ravigneaux type planetary gear set and solved analytically. The shift characteristics of each element of planetary gera set during gear ratio change are investigated by considering the torques and velocities of input, reaction and output elements.