Abstract In the present study, the effects of normal and through-thickness shear (TTS) stresses are simultaneously considered to predict the generalized forming limit diagram (GFLD) of AA3104-H19 using Yld96 [1], Yld2004 [2] and Yld2011 [3] anisotropic yield criteria. For this purpose, considering the general stress state, including the normal and through-thickness shear stresses, the modified Marciniak–Kuczynski (M–K) model is employed. The Newton–Raphson numerical method is applied to solve the nonlinear equations set, and then the forming limit diagram (FLD) and forming limit stress diagrams (FLSD) are computed. First, the forming limit curves are presented by considering the through-thickness shear stress, and then the generalized forming limit curves are presented by applying the normal and through-thickness shear stresses simultaneously. The results show that the through-thickness shear stress has positive sensitivity on the limit strains. Also, the normal stress is more efficient than the through-thickness shear stress on the formability of the plate. Comparison between the results indicates that the predicted limit strains by the Yld2011 anisotropic yield function are lower than those predicted by Yld96.