For the safety of salt rock underground gas storage cavern, uncertainties of material parameters and their influence to structure must be considered. In this paper, random field method is used for failure probability analysis of gas storage cavern. Random field model of material parameters is introduced firstly, local average method is used in discretization of random field, then Monte-Carlo stochastic finite element method is used in failure probability calculation. Conclusions can be drawn as follow: Failure probability in middle part of the cavern is higher than that of upside and underside, and failure probability decreases when operation pressure increasing. Middle part of cavern in release process is the most dangerous. Failure probability of cavern computed by random field model and random variable model based on response surface method are campared. It is obviously that failure prabability computed by random field is lower than that of by RSM. As variation coefficient and fluctuation range increasing, failure probability of salt rock cavern will increase.