An exact solution of the problem of complex shear of a half-space containing an angular groove, is obtained for the strain-hardening law given by (1.1). The latter relation was used earlier to analyze the state in the neighborhood of the weak concentrators, within the framework of the approximate, semiinverse method of V.V. Sokolovskii [1]. Other examples of the problems of grooves which admit closed solutions are shown, and the method of P -analytic representations of solutions given in [2] is used. Applications to similar problems under different laws of strain-hardening are given in [3].