A model for hillock growth in thin films such as those of lead and tin is developed. It is proposed that hillock growth is a form of stress relaxation in which atomic species diffuse along the film‐substrate interface to the base of the hillock. The latter extrudes out along the grain boundaries connecting it to the rest of the film. The stability and kinetics of this process are considered. Taking into account Nabarro‐Herring diffusion creep as a parallel stress relaxation mechanism observations such as an incubation period for hillock growth and the effects of film thickness on hillock density are accounted for. In addition, observations on lateral growth of hillocks and unusually tall hillocks (whiskers) are interpreted within the framework of the present model.