As a specific instability of rock slope, a flexure toppling of rock slope is different from the sliding, and its failure mechanism has not been clarified yet. It is well known that the flexure toppling behavior is influenced by the geology structure significantly. A numerical method based on continuum theory does not seem to work well to simulate the phenomenon. By using a discrete element method (UDEC), the flexure toppling mechanism is studied, and the critical parameters are discussed for a future large slope cutting. Firstly, a numerical analysis is carried out to simulate the flexure toppling failure phenomenon, which happened during the construction site at first. Secondly, a series of numerical analysis have been carried out further in order to find out the critical geometry parameters of the slope for flexure toppling prediction. A significant slip behavior is found between the blocks in the UDEC model, and typical flexure failure phenomenon is reproduced in the simulation. According to the numerical results, a thinner spacing of joints leads to a trend of flexure toppling for the same geometry parameters of the dip and cutting gradient. The toppling failure is related with an alternate relationship between the joint dip angle and the gradient of the cutting slope. With a non-dimension parameter  is defined from the potential failure zone, a new approach is proposed to analyze the slope stability of jointed rock mass