This paper is devoted to developing a yield criterion that can model the asymmetry and anisotropy in yielding of pressure insensitive metals,in terms of accuracy and simplicity of formulation.First,a new isotropic yield criterion,which can model the asymmetry in yielding of pressure insensitive metals,is proposed.Further,using Cazacu’s generalizations to anisotropic conditions of the invariants of the deviatoric stress,the proposed isotropic yield criterion is extended to orthotropy.The proposed anisotropic criterion has a quite simple form,and the number of material constants involved is only half of that of Cazacu’s(2004) yield criterion.Compared to Hill’s(1948) yield criterion,the proposed anisotropic yield criterion has three additional constants,which are used to model the tension-compression asymmetry of materials.All the material constants involved in the criterion can be determined by simple tests.The proposed criterion reduces to Hill’s(1948) yield criterion if the tensile and compressive yield stresses are equal.In other words,the proposed anisotropic yield criterion can be considered as an extension of Hill’s(1948) criterion to tension-compression asymmetry materials.The anisotropic yield criterion is used to describe the plastic response of Cu-Al-Be shape memory alloy(data after Laydi and Lexcellent) and Ni3Al based intermetallic alloy IC10 sheets.It is shown that the proposed yield criterion can describe very well the asymmetry and anisotropy observed in those materials. This paper is devoted to developing a yield criterion that can model the asymmetry and anisotropy in yielding of pressure insensitive metals, in terms of accuracy and simplicity of formulation. First, a new isotropic yield criterion, which can model the asymmetry in yielding of pressure insensitive metals, is proposed.Further, using Cazacu’s generalizations to anisotropic conditions of the invariants of the deviatoric stress, the proposed isotropic yield criterion is extended to orthotropy. The proposed anisotropic criterion has a quite simple form, and the number of material constants involved is only half of that of Cazacu’s (2004) yield criterion. Compared to Hill’s (1948) yield criterion, the proposed anisotropic yield criterion has three additional constants, which are used to model the tension-compression asymmetry of materials. All the material constants involved in the criterion can be determined by simple tests. The proposed criterion reduces to Hill’s (1948) yield criterion if the tensile and compressive yield stresses are equal. In other words, the proposed anisotropic yield criterion can be considered as an extension of Hill’s (1948) criterion to tension-compression asymmetry materials. The anisotropic yield criterion is used to describe the plastic response of Cu-Al- Be shape memory alloy (data after Laydi and Lexcellent) and Ni3Al based intermetallic alloy IC10 sheets. It is shown that the proposed yield criterion can describe very well the asymmetry and anisotropy observed in those materials.