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This paper proposes a numerical approach devoted to the investigation of thesub-surface crack propagation mechanism in gear pairs having crossing axis (i.e hypoid gears).Starting from an accurate 3D description of the complex gear tooth geometry, a numericalanalysis carried out by means of an advanced contact solver allows obtaining, over the entiremeshing cycle, the contact pressure distribution and the displacement field in the uncrackedtooth. Then, such displacements are applied as boundary conditions to a second finite elementmodel of the cracked zone, being the aim the stress intensity factor calculation for the mode I,II, III along the crack front. At this point it is possible to examine the crack growth mechanism:the maximum shear SIF range and the maximum tensile SIF range are computed andconsiderations about direction of crack propagation are drawn. As application of thisapproach, a circular sub-surface crack in a real hypoid gear of a truck differential transmissionis analysed.