A multiaxial fatigue failure criterion is proposed based on the strain energy density damage law. The proposed criterion is hydrostatic pressure sensitive; includes the effect of the mean stress, and applies to materials which do not obey the idealized Masing type description. The material constants can be evaluated from two simple test results, e.g., uniaxial tension, and torsion fatigue tests. The predicted results are compared with biaxial tests and the agreement is found to be fairly good. A desirable feature of this criterion is its unifying nature for both short and long cyclic lives. It is also consistent with the crack initiation and propagation phases of the fatigue life, in the sense that both of these phases can be related to the strain energy density either locally or globally.