Based on the experimental and theoretic studies of the frictional materials in literatures, a generalized non-linear strength theory is presented. The generalized strength theory has the same mathematical form as classical Drucker-Prager strength (D-P) criteria. It describes strength characteristics of various materials using a unified formula, and it includes or approximates numerously present strength criterions. The shape of generalized Drucker-Prager (GDP) criteria is convexly smooth curve between the classical D-P criteria (upper bound) and the external contour line of Mohr-Coulomb (M-C) criteria (lower bound) on the deviator-plane, and a straight line on the meridian-plane. Through variation of parameters in the criteria, a series of criterions ranging between these two bounds may be introduced by the unified strength criteria, and the different strength properties of various materials were denoted.