Nowadays the forming limit curves is very useful in forming of metal sheets and the effect of yield criteria is one of the most important parameters in prediction of the limit strain especially in anisotropic aluminum sheets. In this paper, first the effects of advanced BBC2008, Soare2008, Plunkett2008 and Yld2011 yield criteria on limit strain calculation and then on forming limit stress diagram will be investigated. Plastic instability model is studied based on Marciniak-Kuczynski model and the non-linear equations are solved by using Newton-Rophson method. These functions are used to evaluate the limit forming predictability of AA2090-T3 aluminum sheet based on the Swift hardening law and is compared with the forming limit curves predicted by Hill’s 1948 classic yield criterion. It was observed that the classic yield functions is not appropriate for anisotropic aluminum sheets forming estimation. Numerical results obtained from the forming limit diagram for AA5754 with Plunkett2008 yield function and Swift hardening law, although the experimental results confirm at close range to plane strain case, but CPB06ex2 yield criterion to predict the behavior of anisotropic aluminum sheets. The limit strain prediction for AA3104-H19 by using Yld2011 yield criterion and Voce hardening law show better conformity with experimental results.