This study established the fuzzy logic modeling of the stochastic finite element method based on the first-order approximation theorem. Fuzzy mathematical models of safety repertories were incorporated into the stochastic finite element method to analyze the stability of embankments and foundations in order to describe the fuzzy failure procedure for the random safety performance function. The fuzzy models were developed with membership functions with half depressed gamma distribution, half depressed normal distribution, and half depressed echelon distribution. The result shows that the middle region of the dike is the principal zone of concentrated failure due to local fractures. There is also some local shear failure on the dike crust. This study provides a referential method for solving complex multi-uncertainty problems in engineering safety analysis.