Elastic-plastic numerical stress analyses and fatigue lifetime predictions are presented for shrink-fit compound tubes containing multiple, axial holes at the interface between inner and outer tube. The holes, which are semi-circular, are introduced initially as periodic notches on the outer surface of the inner tube and an outer plain tube is heated, slid over the inner tube and allowed to cool to achieve the shrink-fit. Residual stresses resulting from interference and operational stress ranges arising from cyclic bore pressurization are calculated and fatigue lifetimes are predicted. Two potentially critical locations for fatigue failure are identified as the bore and the notch root. The predicted lifetimes are compared with earlier work on a similar overall geometry subjected to autofrettage. The critical location is shown to be at the bore and a clear improvement in overall fatigue lifetime is demonstrated for the shrink-fit tube compared with the autofrettaged tube. As the interface radius is reduced, there is a general reduction in the ratio of fatigue stress range at the bore to that at the hole and the possibility of the critical location moving to the notch root. A normalized presentation for design purposes is proposed.