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The crankshaft is one of the most important components of the internal combustion engine and its function is, with the rods, transforming the linear movement of the piston into rotation. Because it is under cyclic loads during all of his life, the main type of failure in these components is due to fatigue. However, as they are subject to complex loads, multiaxial stresses are arose resulting in a problem of multiaxial fatigue. Several approaches about this problem were developed, but until now, there is no universally accepted approach. This paper presents a comparison of some multiaxial high-cycle fatigue criteria based on stress invariants, namely Sines, Crossland and Kakuna-kawada criteria. Initially, some basic concepts about such criteria are presented. To facilitate the understanding of the multiaxial fatigue approach, the paper presents also an analysis of stress and fatigue in a steel axle under bending and torsion in phase and out of phase.