This study is concerned with structural integrity evaluations for the interference-fit flywheels in reactor coolant pumps (RCPs) of nuclear power plants. Stresses in the flywheel due to the shrinkage loads and centrifugal loads at the RCP normal operation speed, design overspeed and joint-release speed are obtained using the finite element method (FEM), where release of the deformation-controlled stresses as a result of structural interactions during rotation is considered. Fracture mechanics evaluations for a series of cracks assumed to exist in the flywheel are conducted, considering ductile (fatigue) and non-ductile fracture, and stress intensity factors are obtained for the cracks using the finite element alternating method (FEAM). From analysis results, it is found that fatigue crack growth rates calculated are negligible for smaller cracks. Meanwhile, the material resistance to non-ductile fracture in terms of the critical stress intensity factor (K$_{IC}$) and the nil-ductility transition reference temperature (RT$_{NDT}$) are governing factors for larger cracks.