The stability of single cavern roof is studied with cusp catastrophe model of large deformation circular plate with fixed supports. The necessary conditions of instability are deduced. Considering the level stress contributed under the weight of strata and geological construction
the cusp catastrophe of connected well roof is analyzed with cusp catastrophe model of beam model. The sufficient and necessary condition of instability is deduced
which is the theoretical base of the cavern’s stability controlling and national strategic oil storage in the cavern.