According to field investigations, the failure surfaces of a large number of hard thin-layered anaclinal rock slopes are bilinear-type surfaces, and the overall failure of such slopes is the results of the evolution of cross joints in most cases. In order to realize accurate positioning of such actual failure surfaces, an optimal method, developed by the limit equilibrium theory and the minimum principle of Pan Jiazheng, for searching the bilinear-type failure surfaces of such slopes, was established. The failure surface was considered to be a surface at which the external force triggering the overall failure of a slope was the minimum value. The failure modes (shear sliding and bending tension failure) of rock strata were determined strictly by the failure criteria, and the amount of the failed strata was obtained accurately through a theoretical derivation with justifiable assumptions. The effects of cross joints on the stability of such slopes were taken fully into account. Based on the present computational framework, comparisons with other studies were carried out by taking Yangtai landslide. The results showed that the failure surface obtained with the proposed method compared well with the actual failure surface of Yangtai landslide and the safety factor of the stability of the slope was credible. Through the sensitivity analysis of the continuous ratio of rock strata, we found that with the decrease of the continuous ratio of rock strata, the safety factor of the stability of the slope decreased, and the slope was subjected to shallow damage.