Abstract. This is the survey of the applications of the potential methods to the problems of continuum mechanics. Historical review, new results, prospects of the development are given.This survey paper is dedicated to the 90th birthday of Victor Kupradze. Therefore we shall cover here mainly questions connected with his scientific interests and dealt with by his pupils and followers. We wish to note specially that V. Kupradze's old works on the application of potential methods to the study of wave propagation, radiation and diffraction problems that had greatly contributed to the progress in these directions will hardly be mentioned.Eight years have passed since our previous survey of the field in question.
1That was the period of great events in our life, change of the outlook, revaluation of many results, the arising of new difficulties in the development of science. The potential method keeps on developing and we do have results obtained in these years which are worthwhile being told about.