Abstract: The landslide is considered as a consequence of catastrophic slide of initially stationary or creeping slope triggered by a small perturbation,such as the effect of rainfall. Presuming that slope is shallow and infinitely long and the slip surface is made up of elasto-brittle medium and strain-softening medium,a cusp model of two control parameters,a and b,is formulated with simple law of mechanics. A fully catastrophe analysis is done for all possible scenarios when a continuous change is imposed to the control parameters. As the slip surface is continuous and erosion due to rainfall occurs,the control parameters of the slip surface may evolve such that a previously stable slope may become unstable (e.g. catastrophe occurs),with a small perturbation imposed. Thus the present analysis offers a plausible explanation to why slope failure occurs at a particular rainfall,which is not the largest in the history of the slope. Through catastrophe analysis,it is also found that a complete evolution of landslide includes five stages:stable~slowing slide~uniform slide~accelerating slide~catastrophic slide.