Monograph by G. I, Savin "Stress distribution near holes" is a significant development of his monograph "Stress concentration near holes," published in 1951 and highly appreciated at one time. This monograph has become widespread, translated into several foreign languages. Despite the current powerful computing technology that allows you to numerically solve many problems, including the problems of the theory of elasticity, it is important to develop methods for approximate solutions for individual classes of problems that would give solutions in the form of some relatively simple analytical expressions.