The stability of rock-mass slopes is a very complicated system which is controlled by lots of factors. It is always a very important research subject to evaluate the slope stability reasonably through some evaluation methods. Based on matter-element theory and dependent function,the extension theory is applied to evaluate the stability of rock mass slope,and the extension method for the stability of rock mass slopes is proposed. Taking a real slope project for example,based on the reasonable selection of evaluation factors of slope stability,an extension model for evaluation of slope stability is built,whose result is contrasted with the fuzzy evaluating one. As a result, it is practical and feasible to apply the extension method to estimate the rock slope stability.