Abstarct: Forming limit diagram (FLD) is a criterion to determine necking initiation under different loading paths on sheet mextal which can be influenced by various intrinsic and extrinsic parameters. In recent years, several investigations have shown that the normal stress applied on sheet surface effects the material formability. This normal stress could be created by high speed impact in the rapid mextal forming processes or by concentrated contact force in incremental forming processes. In the present study, the effect of normal stress on forming limit diagram of anisotropic sheet was investigated. baxsed on well-known Marciniak-Kuczynski (M-K) model, the sheet had a grooved inhomogeneity. Anisotropy was considered as an inhomogeneity and uniform zone by Yld2003 and BBC2003 criteria, and plasticity theorem was used to conduct stress-strain relation in each zone. The equation of strain increments for both imperfect and perfect zone was written by using flow rule and strain compatibility and assuming incompressibility condition and regardless of elastic strain. Then stress components were obtained in uniform zone and by using transformation matrix, the stress components were obtained in inhomogeneity zone too. Strain increments were calculated in each zone by using equilibrium equation and Newton-Raphson method and this process continued to reach plastic instability. Experimental data’s of other studies were used for BBC2003 and Yld2003 to verify numerical code in the present study respectively for AA6111-T43 and AA5182-O aluminum alloys. Then, forming limit diagrams strain and stress baxse of these two alloys for different normal stresses were obtained.