The importance of the problem of plastic material flow through a converging channel is due to the extensive use of this method for deformation in many production processes (metal forming, discharge of loose materials from bunkers, etc.). In the last ten years this problem has come the attention of researchers. This attention is justified by new test data [I, 2] clearly showing the asymmetry of these flows. Flow asymmetry is due to localization of deformation, i.e. formation of isolated slip lines which break down the deformable region into individual blocks sliding over each other. This fact has placed in doubt the universality of theoretical solutions based on the hypothesis of radial (symmetrical) flow of material particles. In many recent works (e.g. [3, 4]) a study has been made of features of the block structure of material and engineering methods axe suggested for working out the problem where there is use of some ideas about the size of blocks which is one of the main factors in obtaining a numerical result. It is natural that since the relationships of solid material theory do not contain a dimension of length in 'pure' form the sizes of blocks should be determined by material properties and the geometry of the problem, in particular by the sizes of the inlet and outlet holes of the converging channel. From this point of view it is interesting to construct an asymmetrical solution of the problem of limiting equilibrium for plastic material in a converging channel under the action of an applied load (Fig. 1). The solution is constructed on the basis of limiting analysis theory, i.e., theorems about the upper estimate of limiting load P [5]. The material described by the model is an ideally incompressible rigidly-plastic body (the St. Venant-Mises model). In the prescribed kinematically acceptable field of velocities v(k) the limiting load is determined from the equilibrium equation in integral form