In this paper, effect of advanced yield criteria including BBC2003, Yld2004 and BBC2008 are studied using Swift hardening law on determination of limit strains based on Marciniak–Kuczynski (M-K), Swift’s diffuse necking and Hill’s localized necking models. These models are used to assess the formability prediction of orthotropic AA2090-T3 and AA6111-T4 sheets. The Portevin-Le Chatelier effect on formability of AA5182-O sheet is also studied. The sensitivity of Marciniak–Kuczynski model to the initial imperfection factor is investigated and the effect of this parameter on prediction of forming limit diagram has been shown. Study of the effect of yield criteria exponent on formability shows the higher exponents which are recommended for FCC metals have higher forming limits in comparison with lower exponents adopted to BCC metals. The effects of strain hardening coefficient and anisotropy are studied too. The results show that the increase of strain hardening exponent improves the formability, while the PLC effect and increase of anisotropy coefficient reduce it. Experimental results show better conformity with M-K model at the right side of FLD and with Hill’s localized necking model at its left side.