Abstract: An impact damping system for application to sport shoes having a hollow housing of flexible elastomeric material which is softer and more resilient than the insole material of the sport shoe which it is to be removably placed in a cavity in the heel area of the shoe. The inner and outer surfaces of the housing side which are smooth and homogeneous, and there is a top cover with an overhang lip which rests on the insole. One or more replaceable damping discs are inserted into the housing and are held therein by the cover which has downwardly extending pins to engage a groove in the disc and a peripheral flange at the lower end of the housing.