The stagnation phenomenon of isotropic hardening is observed in the cyclic loading behavior of metals. An extended formulation of this phenomenon is formulated so as to describe the smooth evolution of isotropic hardening by incorporating the concept of the subloading surface, which falls within the framewodc of stress space formulation. In addition it is furnished with the controlling function of the isotropic hardening stagnation variable and thus it does not require any return-mapping algorithm.