Vestnik of Samara University. Natural Science SeriesVestnik of Samara University. Natural Science Series2541-75252712-8954Samara National Research University471110.18287/2541-7525-2013-19-9.2-55-62TASK ON INDENTATION OF SMOOTH PUNCH OF AN ARBITRARY FORM IN PLANE VIEW IN HARD PLASTIC HALF-SPACEVlasovaI.A.morenov.sv@ssau.ruSamara State University02092013199.255620506201705062017Copyright © 2013, Vlasova I.2013In the work the general properties of equations of spatial problem of the theory of ideal plasticity in the condition of Treska plasticity and stressed state that correspond to the ridge of surface of fluctuation are viewed. Singular lines in hard plastic space and solutions in the neighborhood of a singular line that are similar to the expansion in beam series are viewed. On the basis of the developed theory the boundary problem appearing at indentation of punch with smooth basis in a certain plastic body which in the simplest case is a half-space is solved.вдавливание гладкого штампа, штамп произвольной фор- мы в плане, жесткопластическое полупространство, разрывные решения простран- ственных задач, особые линии, особая линия, уравнение особой линии, особые поверхности, краевая задача о штампеindentation of smooth punch, punch of an arbitrary form in plane view, hard plastic half-space, discontinuous solution of spatial tasks, singular lines, singular line, equation of a singular line, singular spaces, boundary problem about punch