Abstract: Traditionally, the calculation of reliability of fuzzy random structures is based on the well-known formulation of probability of fuzzy events. But sometimes the results of this formulation will not indicating the real state of safety of fuzzy-random structures. Based on the possibility theory, a computational procedure for the reliability analysis of fuzzy failure problems and random-fuzzy failure problems of mechanical structures that contain fuzzy variables were presented. A procedure for the analysis of structural reliability of problems of fuzzy failure criterion was also proposed. The failure possibility of fuzzy structures and possibility distribution of the probability of failure of fuzzy-random structures can be given by the proposed methods. It is shown that for the hybrid probabilistic and fuzzy reliability problems, the probability of failure should be suitably taken as a fuzzy variable in order to indicate the real safety of system objectively. Two examples illustrate the validity and rationality of the proposed methods.