The exact solution for the symmetric two impacts/particle/cycle motion of ann‐unit impact damper attached to a sinusoidally excited primary system is derived analytically, and its asymptotically stable regions are determined. Simulated motion on a digital computer and experimental studies with a mechanical model are presented, and they show good agreement with theoretical results. It is found that properly designed multiple‐unit impact dampers are more efficient than equivalent single‐unit impact dampers in regard to vibration reduction and noise level of operating units.