In this article represented are the calculations of initial plastic strips-zones, developed from the corner points of elastoplastic body, which are stress concentrators. With the aim of conducting of these calculations there has been made a transition from the problem on plastic zones to the problems of the theory of elasticity for the wedge-shaped body with the rupture displacement line at the vertex. The exact solutions of the above-mentioned problems are constructed by Wiener-Hopf method. Based on these solutions the lengths of plastic strips and the directions of their development are defined. The results of symmetric cases of the crack end, which is on the media-separating boundary, and the corner point of the hole brings us to a conclusion that the process of development of the initial plastic zone has two stages. At the first stage two side plastic strips are developed from the corner point, and at the second stage one more additional strip, which is considerably smaller than the side ones. In the case of a hole at the second stage before the appearance of the third strip, the side plastic strips deviate from their primary direction of development, thus, leading to the angle increase in between them
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