The instabilities of the rock mass slope with regular weak intercalated layers are discussed；and a slope of swallowtail catastrophe model with the catastrophe theory is established. The jump property of landslide of the rock mass slope with one weak intercalated layer on the basis of slope swallowtail catastrophe mode is studied；and the probability of jump property of the rock mass slope with multiple weak intercalated layers on the basis of extreme points of potentials is qualitatively analyzed. The results show that the latter swallowtail catastrophe model potentials have four extreme points at most，and that the slope state would change with the amount of extreme points of its potentials.