Theoretical studies in the analysis of sheet metal failures are referred to obtain the Forming Limit Diagrams (FLD). Since necking in some processes such as hydroforming can occur at locations where in addition to the in-plane stresses a through thickness compressive stress acts, the plane stress assumption is not proper for these processes. Therefore, in this study, determination of the forming limit diagram with existence of the normal stress is based on the generalized Marciniak and Kuczynski model. Newton-Raphson method has been used to find the set of variables. The structure of FLD prediction algorithm is in a way that it is possible to apply Von Mises and Hill48 yield criterions and different hardening laws. The results show that existence of the normal stress shifts up the forming limit diagram. The increase of limit strain in plane strain state has been investigated quantitatively for better understanding of this effect. The theoretical results have been verified by comparing them with the published experimental data.