Abstract When a building sways due to strong wind or an earthquake, the elevator rope can undergo resonance, resulting in collision with the hoist-way wall. In this study, a hard stopper and a soft stopper comprised of a spring-mass-damper system installed along the hoist-way wall were considered to prevent the string from undergoing excessive vibrations. The collision of the string with multiple hard stoppers and multiple spring-mass-damper stoppers was investigated using an analytical method. The result revealed new formulas and computational algorithms that are suitable for simulating the vibration of the string against multiple stoppers. The numerical results show that the spring-mass-damper stopper is more effective in suppressing the vibrations of the string and reducing structural failure. The proposed algorithms were shown to be efficient to simulate the motion of the string against a vibration stopper.