This paper considers three of the enduring problems of fatigue life estimation: multiaxial loading, stress concentrations and size effects. The work forms part of an extensive investigation which I and my co-workers are conducting into the use of some prediction methods which we call the Theory of Critical Distances (TCD). Data from the literature show that there is a strong effect of hole size on the fatigue limit of specimens containing circular holes. Moreover, this effect is different under different types of loading: in particular, the critical hole size is greater in torsion than in tension. Accurate predictions of this data could be obtained by combining the TCD with a critical plane theory – the Susmel-Lazzarin criterion; to my knowledge this is the first time that this type of analysis has been reported.