By applying a completely reversed uniaxial cyclic strain history, the kinematic and isotropic hardening of 304 stainless steel were determined. An experimental procedure was developed which allowed the size and location of the uniaxial elastic range to be repeatedly determined during any load history. This procedure utilized the capabilities of a computer-controlled materials test system to evaluate in real time when the stress-strain response of a material was no longer elastic. The results of these experiments were compared to a model of kinematic and isotropic hardening of 304 stainless steel developed using another, less direct experimental method.