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Different crack orientations are observed at different locations in thecrack network discovered in the old Residual Heat Removal (RHR) system of nuclearpower plants. The crack orientations are thought to be possibly related to theorientations of the critical plane on which the accumulated fatigue damage is maximumduring the crack initiation period. In this paper, the effects of biaxial mean stress oncritical plane orientations under biaxial fatigue loading conditions are investigatedbased on a combined analytical and computational approach. The analytical solutionsof critical plane orientations using Matake’s and Fatemi-Socie’s crack initiationcriteria are first derived and validated by the computational results obtained from aspecialised C/C++ program and Code_Aster® software. The analytical solutions arethen adopted to study the effects of biaxial mean stress on critical plane orientations.According to the analytical solutions, the critical plane orientations appear to stronglydepend on the dominating stress under biaxial fatigue loading and tend to a constantorientation when the mean stress is sufficiently large. Finally, the analytical criticalplane orientations are correlated with the observed crack directions in the RHR system.