Experiments are conducted on tubular specimens of type 304 stainless steel. The effect of internal pressure is observed under the combined axial‐internal pressure loading. This experiment is utilized to verify the validity of endochronic theory of plasticity which has been shown to give reasonable predictions in a number of other loading conditions. In this investigation, a form of material function is proposed to govern the increment of intrinsic time such that it has a magnitude equal to unity upon reversed loading. The results of this investigation show that the theory generally does lead to favorable agreement with the experimental results. Especially, predictions of the Bauschinger effect are considerably improved.