A series of undrained, partially drained and completely drained triaxial tests were carried out to investigate the influence of drainage boundary conditions on the strength characteristics of saturated clay. The partially drained tests were carried out by controlling the strain increment ratio of the volume and axial strains. The tests investigated the influence of drainage boundary conditions on the mechanical properties of saturated clay including the pore water pressure, the effective stress path and the asymptotic behavior of the -q plane. Based on the asymptotic state and dilatancy characteristics, an asymptotic state constitutive model for the saturated clay was established by introducing the strain increment ratio into the stress path constitutive model. The comparison between experimental results of pore water pressure and effective stress path and simulations demonstrates a good predictive ability of the model. The test results show that the strain increment ratio of saturated clay should be less than 0.3. The drainage condition affects the dilatancy of normal consolidated clay, the effective stress path and the shear strength of soil. With the increase of the strain increment ratio, the pore water pressure and the effective stress ratio of saturated clay decrease but the strength increases. The saturated clay specimen will be in a critical state for a long time when the axial strain of the specimen reaches 3%, and the change in drainage conditions can inhibit or accelerate the failure of the soil.