The maximum principal stresses, von Mises effective stresses and principal facet stresses at the time of creep rupture were compared in uniaxial, biaxial, and triaxial stress states for AZ31 magnesium alloy. The creep rupture of this alloy was experimentally controlled by cavitation, which was the result of a low damage tolerance, $lambda$. Creep deformation could be correlated with the von Mises effective stress parameter. The failure-mechanism control parameter governing the stress state coincided with the experimental results of the rupture of the materials under multi axial stress states. Finally, the theoretical prediction based on constrained cavity growth and continuous nucleation agreed with the experimental rupture data to within a factor of three.