Abstract: Soil is a kind of typical friction material, while natural rock have certain cohesive properties and metal is a kind of completely cohesive material. Based on the analysis of three typical material strength criterion expressions, namely SMP, Lade-Duncan and Extended Von-Mises criterion, an extended criterion, VML criterion, is proposed by using the invariant expression of stress tensor, which can be degraded to the above three typical criteria respectively. In the deviatoric plane, the new criterion can be adopted to describe a variety of opening forms from curved triangle to circle, and in the meridian plane, the power function is adopted as the failure criterion formula, which can be used to describe the nonlinear property of the influence of hydrostatic pressure on the strength characteristics. As for the yield behavior of soil, geomaterials have typical compression-shear coupling characteristics. Therefore, in order to describe the volumetric coupling phenomenon under the two paths of shear and isotropic compression conditions, the droplet yield surface is adopted as the yield criterion. For the section shape on the deviatoric plane, the distribution and characteristics of the strength curve in the deviatoric plane with a fixed hydrostatic stress are discussed, and the influence of the stress Lode angle on the concavity and convexity of the strength curve in the deviatoric plane is discussed. Finally, the new criterion is used to verify the failure and yield test results of various materials. The comparison between prediction and test results have been employed. The comparison results have demonstrated the rationality of the proposed VML criterion.