Directional drilling of complementary holes in a cased well is an effective method of restoring decommissioned, emergency and abandoned wells. It enables the possibility to save on drilling new oil and gas wells. Today, sidetracking is considered to be the most efficient technology which makes use of milling casing window. Cutting into the column wall is a very important process. The milling cutter makes a slot-like hole in it due to the force response of the wedge deflection device in the casing. The upper part of the hole becomes elliptical with a smooth contour due to the small angle of the wedge during the axial moving of the tool. At the same time, the lower edge of the hole is straight and forms right angles with its side edges.  The vertices of these angles create a stress concentration in the wall, weakened by the hole, under the condition that a significant tensile force of its own weight acts on the casing. These stresses reach their maximum values in those pipe cross-sections where the window width becomes maximum (design), and their area is the smallest one. The topicality and novelty of the solved problem lie in studying the stress-deformed state of the casing pipe under tension while cutting a window, close to a rectangular shape, in its wall, as well as in calculating the maximum stresses that arise around the right angles of the hole. These solutions make it possible to specify stress concentration factors depending on the geometrical parameters of the hole, and thereby ensure the development of engineering methods for designing a trouble-free process for window cutting in casing pipes. The operating results are as follows: a developed mathematical model of a nonaxisymmetric stress state that occurs during tension-compression of a cylindrical shell with rectangular holes, for which the analytical methods of calculating the stress-strain state of non-thin shells with non-canonical stress concentrators have been used, and theoretical and experimental studies of the stress concentration in the walls of this shell.