Abstract: Aiming at the support crushing disasters in proximity to coal seam beneath a room mining goaf caused by the different pressure time of the roof above pillars and the immediate roof,according to the nonlinear variation of the pillars’ instability failure under the influence of the overlying load,a system mechanics model composed of roof-pillars-gangue was established.In addition,by using the cusp catastrophe theory,the instability mechanisms of the system under the linear loads were studied,the necessary sufficient condition for instability failure of the system and the formula of the jump value and the releasing energy of displacement of pillars were gained,and the main factors for instability failure of the system were analyzed.The results show that the unstable failure of pillars leads to the support crushing disasters.By using the energy method,the attacking dynamic factor and the working resistance of support were calculated.The rationality of the theoretical derivation has been verified by an engineering example.