In spite of the great number of high cycle multiaxial fatigue in the literature, none predicts the difference that exist between the endurance limits in tension, four point rotative bending and four point plane bending. An enerdy based criterion based on a new concept using the strain energy density is proposed in the paper. This new calculation method explains the previous differnces by taking into account the volumic distribution of the strain energy density around the considered critical point in fatigue. This method, available now under fully reversed mutiaxial loadings, also takes into account the stress state triaxiality. Under combined plane bending and torsion the predictions of the new proposal lead to Gough and Pollard's ellipse quadrant for ductile materials and lead to a curve close to an ellipse arc for brittle materials. Under other multiaxial loadings, predictions are always close to an ellipse quadrant dependent on the loading mode. This method has been tested on smooth cylindrical specimens with several materials; calculations are in very good agreements with multiaxial experimental data.