In this study, the effect of a compressive normal stress has been considered in the determination of forming limit diagrams and forming limit stress diagrams to predict neck initiation failure in tube hydroforming of T-shaped parts. Computation of the forming limit diagrams and FLSDs is based on the generalized Marciniak and Kuczynski method to consider the existence of through-thickness compressive normal stress. The proposed forming limit diagrams and FLSDs were used in conjunction with ABAQUS/EXPLICIT finite element simulations to predict the onset of necking in tube hydroforming of T-shaped part. The amount of calibration pressure and axial feeding required to produce an acceptable part in finite element method was compared to published experimental data, and a satisfactory agreement between the FEM and test results has been achieved. Therefore, the present approach can be used as a reliable criterion to design tube hydroforming processes and reduce the number of costly trials.