A thermal cycling fatigue crack growth experiment has been performed on austenitic stainless steel plates in which a semi-elliptical surface crack grows through a surface layer experiencing cyclic plasticity. Linear elastic fracture mechanics crack growth assessments over-predict the surface growth and under-predict the through thickness growth. An alternative crack growth analysis has been performed using a pseudo stress intensity factor which is closely related to a strain intensity factor. The pseudo stress used to derive the pseudo stress intensity factor is calculated from uncracked body inelastic finite element analysis. It is demonstrated that a much improved prediction of fatigue crack shape can be made provided that the effects of crack closure are incorporated into the analysis. The method is relevant to leak-before-break and leak tightness arguments where the accurate prediction of through-thickness crack growth is particularly important.