Theoretical strength of solids is defined as the ultimate strength beyond which plastic deformation, fracture, or decohesion would occur. Understanding the microscopic origin from quantum mechanics and thermoelastic formulation is of great importance to mechanical properties and engineering design of various solids. While quite a few theory models have been made in the past century by several generations of scientists, including Frankel and Born, a general and convincing framework has not been fully established. We study this issue from three respects: (1) Unify various elastic stability criteria for solids that determine an upper bound of theoretical strength; (2) with ab initio method, we test the elastic stability conditions of crystal Au. The phenomenon of bifurcation is observed: under hydrostatic expansion, the rhombohedral modulus reaches zero first of all; while under uniaxial tensile stress, the tetragonal shear modulus first reaches zero; (3) propose a nonlinear theoretical formulation of stability criterion. As an analytic method, this scheme is quite simple, in the mean time, it saves computation resource.