Abstract：The clear conclusions about the stability of soil slope have not been achieved nowadays，such as the slipping surface goes through the slope foot or not. The difference of slipping force to resistance force，not the ratio as usually，is used as an evaluation index of the soil slope stability，and the limit curve，along which the evaluation reaches to its maximum value，is studied with calculus of variations. The slipping surface in a soil slope is the limit curve of which the evaluation approaches to zero. On this definition，it is proven that all the slipping faces will pass through the slope foot，and the critical height of soil slope is a formula of cohesion，internal friction coefficient，gravity and the slope angle. If there is a safety coefficient in the stable analyses，the critical height can be calculated with the same formula in which the cohesion and internal friction coefficient is divided by the safety coefficient. Lines are special circles，and circles are special continuous curves，so the critical heights for them become smaller one by one. As for vertical slope，the difference among the three critical heights are not great. But for general slopes，the lowest point in limit curve is below the slope floor，which results in great slipping force around slope shoulder. Meanwhile，the resistance force from the negative slope near the foot is small. So its critical height is much lower than that from plan failure.
