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Calculation of the material fatigue life under multiaxial random loadingneeds, among others, application of the failure criteria based on the expected positionof critical planes. It is convenient to determine those positions in relation to theprincipal stress or strain axis directions. In the paper the expected directions of theprincipal stress under proportional and non-proportional loading have been determinedby averaging the instantaneous values of the Euler angles with use of special weightfunctions. The known weight functions based on the stress parameters have not beenefficient for each loading or material. Thus, the authors considered new weightfunctions based on the energy parameters. The presented forms of weight functionswere verified in tests of 18G2A steel. It has been shown that the fatigue fracture planedirection under multiaxial loading can be efficiently determined on the basis of anaveraged direction of the maximum principal stress including a suitable weightfunction.