Abstract: Based on the equivalent transformation from fuzzyvariables to random variables and the finite element method (FEM)calculation, a practicalcriterion, with the relative probability importance as a measure ofthe failure mode, is presented to enumerate the fuzzy-random significantfailure modes for the fuzzy-random reliability analysis of complicatdstructures. Not only randomness but also fuzziness in the basic variables areconsidered in the criterion. The mean values and the coefficientsof variation in the basic random variables are included in the relativeprobability importance of the failure mode, as well as the equivalent mean valuesand the equivalent coefficients of variation in the basic fuzzy variables.With a high precision, the criterion can greatlyreduce the computation cost and the possibility of missing importantfailure modes. The fuzzy-random reliability analysis for the shaft structureof an airplane is made to illustrate the rationality of the present method.