The stress relaxation of rock is related to the long-term stability in all kinds of rock engineering, and the influence of water cannot be ignored. The tests of single-stage stress relaxation and cyclic stress relaxation for dry and saturated sandstone were conducted, and the differences of relaxation behavior between the two states of samples were analyzed contrastively. The generalized Maxwell relaxation constitutive model with four elements was adopted for the implementation of numerical verifications. The results show that: 1) The sandstone in both states represents the typical incomplete attenuation characteristic; 2) under the same strain ratio, the final stress relaxation degrees in saturation state are slightly higher. The difference is mainly reflected in the development of stress relaxation, which is deeply affected by the weakening of water; 3) in the peak stress cyclic relaxation tests, the ductility of saturated samples increase due to water weakening and internal energy dissipation. Although the stress relaxation degree of dry samples is higher than that of saturated samples, the results are opposite for the number of cycles and axial strain at final failure; 4) the constitutive model of four-element generalized Maxwell stress relaxation can completely describe the whole process and the trend of single-stage stress relaxation for sandstone with high accuracy.