This paper presents a stability analysis for fractal cracks. First, the Westergaard stress functions are proposed for semi-infinite and finite smooth cracks embedded in the stress fields associated with the corresponding self-affine fractal cracks. These new stress functions satisfy all the required boundary conditions and according to Wnuk and Yavari's embedded crack model they are used to derive the stress and displacement fields generated around a fractal crack. These results are then used in conjunction with the final stretch criterion to study the quasi-static stable crack extension, which in ductile materials precedes the global failure.