This paper proposes a yield function to model sheet metal strength between shear and plane strain tension. The function is expressed as an equation of the three stress invariants to take into account the pressure sensitivity, the Lode dependence and the strength-differential effect on material strength. To validate the accuracy of the formulated yield function, experiments are conducted with the designed specimens to characterize the mechanical behavior of AA7075 and QP980 sheet between shear and plane strain tension. The yield function and the combined Swift-Voce hardening law are iteratively calibrated by using an inverse experimental-numerical scheme. The calibrated constitutive equations are utilized to numerically predict the load-stroke responses of different tests. The numerical prediction demonstrates that the proposed yield function calibrated by the inverse engineering approach can accurately describe the material strength in various loading conditions from the onset of yielding to ultimate rupture. Accordingly, the proposed yield function is recommended to model material strength under various loading conditions, and the inverse engineering approach is suggested for the calibration of its parameters.