A new strength criterion defining the general ultimate stress of concrete is presented. A linear interpolation shape function in the deviatoric plane based on the Unified Twin-Shear Strength theory for all types of materials is developed. The criterion for concrete adopts the generalized linear interpolation functions in the deviatoric plane and the empirical formulas proposed by Guo et al. for tensile and compressive meridians. The construction of the criterion requires only 1 parameter, the uniaxial compressive strength f-sub-c. The criterion can be useful in numerical analysis as well as in practical engineering.