Abstract: Surrounding rock system of the roof-pillars is simplified,the pillar was approximated to the elastic element and the plastic softening element connected in series,the roof and floor-pillar system is established.The cusp catastrophe model is established based on the catastrophe theory,which could induced rock burst by roof-pillar rock system instability,and then the necessary and sufficient conditions of pillar destabilization is obtained.Analysis of the influence factors of instability of pillar is done,which can provide a reference for designing of the actual production.