In this paper a linearized and unified yield crierion of metals is presented,which is in a form of a set of linear functions with two pararneters.The parameters are expressed in terms of tension yield stress and so-called "shear-stretch ratio" and can bereadily determined from experimental data.It is shown that in stress space the set of yield functions is a set of polygons with twelve edges located between the Tresca's hexagon and twin-shear-stress hexagon[1].In this paper the present yield function isused to analyse the prestressiap loose running fit cylinders.