The extensive fabrication of aluminum-alloy sheet in the aircraft industries has revealed the lack of fundamental knowledge regarding the phenomena which explain the performance of metals under various stress and strain states. Previous investigations appear to have neglected entirely both the effects of the part geometry and the fact that the strength of the metal and limit of forming are frequently determined by a process of instability, or “necking,” rather than by the process of fracturing. In this paper a theory of necking is developed in order to predict the forming limits for various stress or strain states based upon an analysis of the true stress-strain curve in pure tension. A criterion for necking is advanced, based upon the maximum-load (or pressure) conception of instability, and is applied to different geometrical shapes formed at room temperature. Future publications will present, in support of the criterion advanced, experimental analyses of the forming of different geometrical shapes under various loading conditions and stress and strain states.