<p>Uncovering and describing the anisotropic-asymmetric hardening behavior of Mg alloys is very critical to their engineering application. The research proposed a three-dimensional yield function (asyHill48) by incorporating three linear terms into the anisotropic Hill48 yield function. The material parameters are analytically calculated based on the hardening curve under various axial loadings. The effect of the first stress invariant on the yield locus is analyzed to show the ability to describe the strength differential (SD) effect. The mechanical property of the Mg-Gd-Y alloy is strongly dependent on the loading direction and exhibits a negative SD effect related to strain. The anisotropic-asymmetric hardening behavior of the Mg-Gd-Y alloy and an as-extruded Mg-Al-Zn-RE alloy under the three-dimensional state is accurately captured by the asyHill48 yield function without considering the convexity of the yield surface. The proposed three-dimensional analytical model describes the mechanical behavior in the three-point bending process with a prediction accuracy that is better than that of the Hill48 yield function. The research provides an analytical model for the forming process design of metal with three-dimensional anisotropic-asymmetric hardening behavior.</p>