The macroscopic relationships between true stress and true strain for pure metals such as Al and Cu and for Al-Mg alloys were investigated both experimentally and theoretically. Experimental results showed that for pure Al and Cu the relationship between stress and strain may be accurately described by an exponential-power law constitutive relationship over a wide range of strain. The validity of the new relationship is supported also by theoretical considerations when taking into account certain conditions appropriate to the main micro-mechanisms of plastic deformation. This new relationship can also be used for a description of the global work hardening of an Al-3%wt Mg alloy.