By considering the modeling advantages of the lower bound finite element limit analysis (LBFELA), the present study introduces a novel and simple technique to analyze the influence of an existing surface crack on the stability of cliff having an undercut. By incorporating the different boundary conditions along the discontinuity edges, two types of existing cracks, i.e., fine and separated, are considered. The rock mass at collapse is modeled as the Generalized Hoek-Brown failure criterion with the help of power cone programming (PCP) in the self-developed LBFELA code. The variation in stability caused by the presence of both types of surface crack and undercut is presented in terms of a stability number, σci/γH; where σci represents the uniaxial compressive strength of rock sample, γ is the unit weight of the rock mass, and H is the height of cliff. The variation in the magnitudes of σci/γH is presented as design charts by considering the different depths of surface crack and the various strength parameters of rock mass. The reduction of stability is observed in the presence of surface crack and undercut. As expected, in the presence of a separated surface crack, lower stability is found in comparison with the presence of a fine surface crack on cliff. In addition, the prediction equations for the obtained stability number are presented by using both the classification and regression techniques with the help of artificial neural network (ANN). Furthermore, a sensitivity analysis is performed, and it is found that H/vu and GSI are the most sensitive parameters among all the input parameters. Failure patterns are also studied to find the extent of the plastic state during the collapse.