Specimens of 304 stainless steel were tested to failure at elevated temperatures under multiaxial stress states, uniaxial tension using smooth bar specimens, biaxial shearing using double shear bar specimens, and triaxial tension using notched bar specimens. Rupture times are compared for uniaxial, biaxial, and triaxial stress states with respect to the maximum principal stress, the von Mises effective stress, and the principal facet stress. The results indicate that the principal facet stress gives the best correlation for the material investigated, and this parameter can predict creep life data under multiaxial stress states with rupture data obtained with specimens under uniaxial stresses. The results also suggest that grain boundary cavitation, coupled with localized deformation processes such as grain boudary sliding, controls the lifetimes of the specimens.