Impact dampers have been extensively used to reduce amplitude of vibrations of systems subjected to steady state excitations. Presently, a study is made of the general behaviour of a single particle impact damper when the system is subjected to earthquake excitations. Equations of motion have been derived and methods for solu-tion indicated. The extensive use of the digital computers is made to solve the problem. Result's of the analysis are supplemented for the following two earthquakes: I. ElCentro Earthquake of May 18,1940,N-S Component, 2. Taft Earthquake of July 21,1952, S 21 W Component and it is found that impact damping is considerably effec-tive to reduce the response of a system subjected to an earthquake. Shady state test is performed on a single storeyed steel paTtal frame With and without impact damper,