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To consider the uncertainty when determining the values of geo-mechanical parameters, interval values are used to indicate the physical and mechanical parameters of the rockmass. An interval non-probabilistic reliability model of the surrounding jointed rockmass of an underground opening, which can be used when the data are scarce, is developed to evaluate the stability of the rockmass in the Jiaojia gold mine. The calculation results of the interval non-probabilistic reliability are in agreement with the actual situation. Thus, the interval non-probabilistic reliability is a beneficial complement to the traditional analysis methods of the random reliability and the safety factor.