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Abstract The logic and result that slope failure problem has been summed up as cusp catastrophe model research have been analyzed；and the potential sliding zone is supposed to be composed of two media only with characteristic of elasticity and with characteristics of elasticity，hardening and softening. Furthermore，it is pointed out that when slope is rigid body and potential sliding zone is composed of foregoing two media，there are not plenty of elastic energy instantaneous release and abrupt sliding mechanism in the slope failure model，which can not correspond to the action that on cusp catastrophe equilibrium curved surface there are plenty of energy release concomitant with state variable jumping from one sheet to another. The potential function of this slope failure model can not be applied to discussion of the problems about slope failure and slide，because there is only elastic parameter without residual strength parameter of section ① in it. On cusp catastrophe equilibrium curved surface，there are many basic characteristics of cusp catastrophe，such as state variable can jump upward and downward，the parameter of jumping upward lags behind that of jumping downward and system state of upper-lower sheets realize cyclically. The slope failure is irreversible，not only it can not jump backward，i.e. slope recovers original state abruptly again after its failure，but also it has no lag characteristic. Hence，cusp catastrophe can not be used as the mathematical model of slope failure prototype.
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2010, Vol. 29 
