The purpose of the present study is to investigate the effect of specimen thickness on statistical properties of crack growth resistance. In this study, the resistance S$delta$$_h$(x) to fatigue crack growth was treated as a spatial stochastic process. which varies randomly on the crack surface. The theoretical autocorrelation functions of the resistance to fatigue crack growth considering specimen thickness are discussed for several correlation lengths. The main results obtained are : (1) The theoretical autocorrelation functions of S$delta$$_h$(x) are almost independent of specimen of specimen thickness except for the origin. (2) The variance increases with decreasing specimen thickness.