Abstract: For the new subsidence reduction mining technology of the strip type Wongawilli,the instability of coal pillar directly affects the surface subsidence and the safety of surface structures. The cusp catastrophe models of narrow coal pillar and strip coal pillar instability were established based on the catastrophe theory and damage constitutive equa- tion. The engineering stability and catastrophic parameters of coal pillar with the strip Wongawilli were analyzed. The calculating equation of narrow coal pillar and strip coal pillar compression was obtained,and the rationality of results is verified by numerical simulation and engineering example. The results demonstrate that the catastrophic occurrence is decided by the load,the yield stiffness and the compression of peak load if the pillar between mining caves meets some necessary conditions for catastrophic instability. If the catastrophic instability of coal pillar system does not occur,the ratio of mining width to pillar width should be between 0. 16 and 0. 75 when the mining height changes between 2 m to 6 m. The coal pillar remains stable if the rate of its elastic area is more than 17% . And if the ratio of elastic to plastic zone width is less than 0. 21,the catastrophe instability of the strip coal pillar may occur.