In this paper, it is examined the lateral oscillation of the moving elevator rope and cab, using the method of characteristics. We consider forced oscillation of the system composed of a rope with time-varying length and a mass-spring system at a lower end. When the upper end of the rope is excited sinusoidally, the elevator in a high-rise building passses through plural resonance points. First, we show that the rate of the cab's guide spring influences the resonance amplitude. When the natural frequency of the lateral oscillation of a cab is equal to the frequency of excitation, the amplitude of the cab has a maximum value. Next, it is examined whether the sign of the moving velocity influences the amplitude of the lateral oscillation of the cab at a resonance point. Furthermore, it is examined its oscillation mode jumps many times in the going up or down process, because the natural frequency changes in a wide range. These are closely related to the transition of the natural frequency of the system.