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The problem of the contact between a cylinder rolling on a semi-planewith an inclined edge crack is solved by the Weight Function method. The CrackOpening Displacement components were obtained by using the analytical expression ofthe Green’s Function. The Hertzian pressure distribution was assumed as load todetermine the nominal stress distribution in the un-cracked body. The conditions ofpartial crack closure were analysed and the influence on the effective stress intensityfactors KI and KII produced by the normal and tangential forces acting on the closedportions of the crack were included. By considering different friction conditionsbetween the crack surfaces, the evolution of KI and KII during a typical loading cyclewas analysed. The effects of the crack inclination and friction on the crack surfaceswere investigated