There is uncertainty in the analysis of the stability of karst roof under pile tip. The interval numbers were used to express the calculation parameters. And the method to determine the interval numbers was proposed by the comprehensive application of interval mathematical theory, rock mass rating index (RMR) and Hoek-Brown empirical strength criterion. Secondly, the limit equilibrium analysis model of karst roof under pile tip was presented on the basis of the present study. The model can consider the action of punching shear, shearing and bending at the same time. Thirdly, the performance function was proposed to evaluate the reliability of the stability of karst roof under pile tip. The non-probabilistic reliability analysis method for stability of karst roof under pile tip was finally founded. This method is proved to be rational and feasible with engineering case analysis, and it provides a new uncertain analysis method for the stability evaluation of karst roof under pile tip.