To investigate the instability of super-long pile under lateral dynamic load, the double cusps catastrophe model to analysis the dynamic stability of super-long pile is established by catastrophe theory. The mechanism of stability of super-long pile under lateral simple harmonic load is analyzed and the coordinates of two cusps is derived. The effects of nonlinear coefficient 滋and frequency ratio on amplitude of super-long pile are analyzed. The analysis of the parameters shows that: when nonlinear coefficient between two cusps,continuous change of 浊can arise abrupt change of amplitude, that is, produce jumping, which is the mechanism of lateral instability of super-long pile.