Abstract: The roof rock was assumed in the elastic state,established the mechanical model of coal pillar and roof system. Based on the mechanical model,by applying catastrophic theory,a cusp catastrophic model for failure instability of strip coal pillar was set up,the formula of fully essential condition for instability failure of strip coal pillar was derived. The analysis show that coal pillar instability connect with the failure degree of strip coal pillar roof,because of influence by mining,roof incidence the plastic zone,the plastic zone more width,its elastic stiffness k_d more small,the more easy occurrence catasophic instability.