A complex safety surface of the quality of deep drawn steel pieces is built on the basis of 45 numerical eperiments. This surface is a combination of subsurfaces reflecting the effects of plastic strain localization and stability loss of the form change of circular blanks. The safety zone of quality is disposed below the safety surface. Two parameters of quality are proposed. Their high values lead to dispositions of drawing forces out of the safety surface of quality and to disturbance of quality, respectively. The results obtained for the safety zone and reported in this paper give an opportunity of estimation in advance phenomena as plastic strain localization and stability loss during the blank form changes. The safety surface of quality is given and respective illustrative examples are presented. and Obsahuje seznam literatury