The loading history-dependent forming limits have been computed for sheet metals undergoing various combinations of plane-stress loading conditions. The analysis method is essentially an extension of Marciniak and Kucźynski’s inhomogeneous model, except that the roles of isotropic and Prager-Ziegler kinematic hardening have been examined in detail while the flow theory of plasticity is applied. A suitable modification of the constitutive equations for the kinematic hardening model converts the rate form of the constitutive equations into the finite-increment form which satisfies the yield criterion precisely. Representative combinations of strain history consisted of an initial proportional straining to either a fixed strain state or different levels of strain state followed by continued loading under different conditions of strain ratios. Comparison of computed forming limits with available experimental data shows that the ultimate choice of either an isotropic or a kinematic hardening model is dependent on a specific combination of strain history and the material properties.