Abstract: Vertical instability of drilling shaft lining is a mechanical problem with gradual change to abrupt change. How to combine traditional mechanical model with modern mathematical methods to achieve quantitative research on this instability mechanism analysis is the theoretical innovation on vertical stability of drilling shaft lining structure and the research content of this paper as well. When the shaft suspended and sunk to the bottom of the well, a certain amount of elastic potential energy is accumulated. At this time, the state of stable equilibrium is dynamic, and the shaft may tilt, slip, or even lose stability., and strengthened monitoring and effective prevention is necessary. In this paper, based on the theory of catastrophe and the mechanics model of shaft wall suspension and subsidence, the total potential energy function and the cusp catastrophe model for vertical instability of shaft lining were established. According to the equilibrium surface and bifurcation point equation of the model, the quantitative determination conditions of the instability are given. The results show that the values of the control variables m and n directly determine the stable equilibrium state of the shaft wall. When Δ>0, the control variable (m,n) falls outside the bipartite point set, the system is located at the upper and lower blade of the equilibrium surface, and the shaft structure is in a stable equilibrium state. When Δ<0 the control variable (m,n) falls inside the bipartite point set, the system is located at the middle of the equilibrium surface, and the shaft structure is in an unstable equilibrium state. When Δ=0, the control variable (m,n) falls on the boundary of the bipartite point set and the structure is in a critical stable equilibrium state. Furthermore, based on thecritical condition of stable equilibrium, the critical depth formula of vertical instability of shaft lining full and non-full water is established. At the same time, in order to popularize the engineering application of the catastrophic model analysis method, the flow chart of instability analysis and judgment is established by using Python language, which provides the theoretical basis for monitoring and forecasting and well type parameter optimization. Combined with an engineering example, it is found that the critical depth based on catastrophe theory in this paper is 0.396% and 7.15% different from those obtained by energy method respectively under full water and non-full water condition. Therefore, the study method of shaft lining structure stability based on catastrophe theory can effectively explain the vertical instability of shaft lining structure.