We study the dynamical phase transitions in the elevator traffic during the morning peak period. We apply the coupled nonlinear map model to the dynamics of M elevators. We investigate the effect of elevator's number M on the dynamical transition. It is shown that the dynamical transitions occur at two stages. The first transition occurs when an elevator carries the full load of passengers. Then, the second transition occurs if all the elevators carry the full load of passengers. The number of riding passengers fluctuates with varying trips. This is due to the deterministic chaos. The motions of elevators depend on the loading parameter, the maximum capacity of an elevator, and the number of elevators. The dependence of the first and second transition points on the elevator's number M is shown.