Abstract: The expressions of the stress component in the plane ( contacting body ) are derived as the frictionally slipping contact arises between a plane and a cylinder on the basis of Hertz theory Distributions of the stress in the plane are analyzed in detail , and their characteristics are presented There exist the maximal tensile stress and the maximal compressive stress in the contacting surface The maximal tensile stress occurs at the edge of the dragging side , and the maximal compressive stress takes place at the area of the leading side Therefore , if the failure in the contact plane is induced by the tensile or compressive stress , it occurs firstly in the contacting surface ; the first crack generation and propagation firstly take place at the edge of the dragging side The maximums of the shear stress , the principal shear stress and the Von -Mises equivalent stress ( when the frictional coefficient is small ) all occur inside the contacting body , and they all exist in the leading side Therefore , The plastic slipping inception firstly takes place inside the contact plane , and then extends to the contacting surface Those conclusions provide a base for the study of the engineering application