Abstract: The hydro-mechanical coupling relaxation characteristics is one of the key factors for long-term safety and stability of surrounding rocks. The hydro-mechanical coupling tests on effective confining pressure laws and sensitivity loading rates of saturated grey sandstone were conducted by the multi-field coupling triaxial test system. According to the relaxation characteristics, the generalized Maxwell relaxation constitutive model with three elements was adopted for the implementation of numerical verifications. The results showed that: 1) In the condition of hydro-mechanical coupling, saturated sandstone had the characteristics of incomplete attenuation relaxation. 2) Under the same effective confining pressure, the relaxation degrees of specimens without pore water pressure were slightly lower than that with pore pressure, while relaxation rates in the steady state were only about 45% of that with pore pressure. 3) The relaxation characteristics of sandstone depended significantly on loading rates. The relaxation degrees and initial relaxation rates increased with loading rates, in which the initial relaxation rates of specimens with the highest loading rate were almost six times rates for specimens with the lowest loading rate, while the relaxation rates in the stead state were no obvious different. 4) The whole process of hydro-mechanical coupling relaxation of sandstone could be accurately described by the three element generalized Maxwell relaxation constitutive model with three elements.