<p>Yield criteria play a central role in capturing the stress state-dependent plastic behavior of lightweight alloy sheets. However, most existing yield criteria that depend on six typical stress states fail to provide convex spaces, making their convexity assessment complicated and limiting their wide applications. To avoid these issues and accurately model the yield behavior of lightweight alloy sheets between balanced biaxial tension and plane strain compression, a new isotropic yield criterion (YC) dependent on six representative stress states with a three-dimensional convex space is proposed in this paper, and the analytical solution for determining its material parameters is derived. The isotropic YC is then converted into two anisotropic yield models using two different approaches, and the performance of the two anisotropic criteria in modeling the yield behavior across the wide stress state range is compared. Furthermore, the isotropic YC is utilized to model the yield behavior of isotropic BCC, HCP and FCC polycrystals. Meanwhile, the converted anisotropic YC, showing better performance and remaining the advantage of having convex spaces, is employed to characterize the yield behavior of AZ31, DP980 and AA5754-O sheets. The applications demonstrate that the converted anisotropic YC is able to effectively model the yield behavior of various metal sheets under different stress states, ranging from balanced biaxial tension to plane strain compression, through an analytical approach, while offering the advantages of providing convex spaces and easy evaluation of convexity.</p>