The impact of the variation of shear strength parameters of soil with depth on the stability of buried foundations has not been thoroughly studied yet. A non-stationary random field model in which the mean and standard deviation of undrained shear strength of soil increase linearly with depth with different degrees was established. In addition, the stationary random field with the same mean of undrained shear strength as the corresponding non-stationary random field was established. The influence of non-stationary random fields with different degrees on the bearing capacity of buried foundations and the failure probability of buried foundations were discussed. The difference of bearing capacity associated with non-stationary random field and its corresponding stationary random field was compared. The results show that when considering the non-stationary of undrained shear strength, the mean value and the difference of bearing capacity of buried footings increase linearly with the degree of non-stationary. The deeper the foundation depth is buried, the more the average bearing capacity increases with the increase of non-stationary degree. Under the same safety factor level (FS >1), the failure probability of the foundation increases with the increase of non-stationary degree. For the buried foundation, at the same level of safety (FS >1), the stationary stochastic field model underestimates the failure probability of a non-stationary field, and the higher the non-stationary state, the larger the estimation error.