The general system of equations describing the smoothing of surface structure in solids under irradiation is formulated. It is shown that under real conditions the system can be reduced to a simpler form which has an exact solution. A general formula describing the smoothing of surface structure with time is derived. As a special case, this formula gives the evolution (smoothing) of the relief in the absence of radiation, which is associated with the difference in curvatures for different roughnesses. The physical reason behind the intensification of smoothing under irradiation is the difference between the positions of the centers of gravities for concentration profiles of vacancies and interstitials. The radiation gives rise to a new type of dependence of the rate of smoothing on the roughness parameters of the surface, which permits the experimental separation of the contribution from radiation to smoothing and simultaneously makes it possible to determine some parameters which are difficult to measure. ©1997 American Institute of Physics.