The yield criteria of geomaterials play a crucial role in studying and designing the strength of materials and structures.The basic characteristics of yield criteria for geomaterials need to be studied under the framework of continuum mechanics.These characteristics include the effects of strength difference(SD) of materials in tension and compression,normal stress,intermediate principal stress,intermediate principal shear stress,hydrostatic stress,twin-shear stresses,and the convexity of yield surface.Most of the proposed yield criteria possess only one or some of these basic characteristics.For example,the Tresca yield criterion considers only single-shear stress effect,and ignores the effect of SD,normal stress,intermediate principal stress,intermediate principal shear stress,hydrostatic stress,and twin-shear stresses.The Mohr-Coulomb yield criterion accounts for the effect of SD,normal stress,single-shear stress and hydrostatic stress,but disregards the effect of intermediate principal stress,intermediate principal shear stress,and twin-shear stresses.The basic characteristics remain to be fully addressed in the development of yield criterion.In this paper,we propose a new yield criterion with three features,that is,newly developed,better than existing criteria and ready for application.It is shown that the proposed criterion performs better than the existing ones and is ready for application.The development of mechanical models for various yield criteria and the applications of the unified strength theory to engineering are also summarized.According to a new tetragonal mechanical model,a tension-cut condition is added to the unified strength theory.The unified strength theory is extended to the tension-tension region. The yield criteria of geomaterials play a crucial role in studying and designing the strength of materials and structures.The basic characteristics of yield criteria for geomaterials need to be studied under the framework of continuum mechanics.These characteristics include the effects of strength difference (SD) of materials in tension and compression, normal stress, intermediate principal stress, intermediate principal shear stress, hydrostatic stress, twin-shear stresses, and the convexity of yield surface. Most of the proposed yield conditions have only one or some of these basic characteristics. For example, the Tresca yield criterion considers only single-shear stress effect, and ignores the effect of SD, normal stress, intermediate principal stress, intermediate principal shear stress, hydrostatic stress, and twin-shear stresses. The Mohr-Coulomb yield criterion accounts for the effect of SD, normal stress, single-shear stress and hydrostatic stress, but disregards the effect of intermediate princ ipal stress, intermediate principal shear stress, and twin-shear stresses.The basic characteristics remain to be fully addressed in the development of yield criterion.In this paper, we propose a new yield criterion with three features, that is, newly developed, better than existing criteria and ready for application. It is shown that the proposed criterion performs better than the existing ones and is ready for application. development of mechanical models for various yield criteria and the applications of the unified strength theory to engineering are also summarized. According to a new tetragonal mechanical model, a tension-cut condition is added to the unified strength theory. The unified strength theory is extended to the tension-tension region.