Abstract: The structural failure is fuzzy as well as random. In this paper, a finite element method and a simulated annealing-genetic algorithm are proposed to determine the structural fuzzy reliability. A modified joint probability density function (MJPDF) is introduced for each failure level such that the most probable point of failure (the design point) is calculated by finding a maximum to this function in the corresponding failure field. The finite element method is used to calculate the load term. Conventional optimization approaches generally have much difficulty in dealing with MJPDF. In this paper the simulated annealing algorithm is incorporated in the generic algorithm to improve the convergence performance of the genetic algorithm. The proposed approach can search for the global optimum more efficiently and effectively, not requiring calculation of numerical derivatives. A fuzzy reliability assessment of a cantilever beam illustrates the application of the method.