Abstract: Based on the theory of multi-phase media continuum mechanics, the coupling instability theory of coal-methane outburst is proposed under finite deformation. From Second Laws of Thermodynamics, mathematical model of coal-methane for coupling instability of solidfluid biphase media is established by using two-order work minimum principle as a criterion for occurrence of outburst. The nonlinear finite element equations are presented. Numerical simulation of a typical outburst is made.