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A curved surface crack was produced during a fretting contactexperiment in titanium. Constant normal contact and material bulk loads werecombined with a cyclic tangential load. The overall crack shape became a part of anellipsoid. It was assumed that the fatigue crack growth followed the direction thatresulted in pure mode I. Thus, the loading on the curved ellipsoidal crack remainedconstant as the crack shape was transformed into that of an elliptical edge crack. Aparametric crack growth description procedure for the elliptical edge crack was used tomodel the crack growth. The growth equations were obtained in terms of the change ofellipse’s semi axes. Finally, the number of load cycles from an initial small edge crackto the final ellipsoidal crack was determined. A crack path prediction based on thelargest normal stress range is included.