<p>This paper introduces, for the first time, a failure risk analysis method for dangerous earth‒rock dams on the basis of element failure probability by combining the finite element discretization technique, the upper bound theorem, the associated non-Gaussian random field theory and the stochastic programming theory. On the basis of the obtained discrete noncommon node triangular elements, a failure risk analysis model is constructed that simultaneously considers the spatial variability in shear strength parameters and the randomness of reservoir water levels. An efficient solving program is developed on the basis of Monte Carlo simulation iteration. To validate the proposed method, a systematic analysis of a specific dangerous earth‒rock dam in Yunnan, China, is conducted. This study demonstrates that the method proposed in this paper can accurately determine the element failure probability of earth‒rock dams on the basis of element velocity information and safety factors. With this information, the calculation of failure risk for dangerous earth‒rock dams is significantly streamlined, thus simplifying the entire process of failure risk analysis. The research findings provide a theoretical basis for the management of such dangerous earth‒rock dams.</p>