Stress relaxation is one of the typical manifestations of soil rheology. For further investigation, drained triaxial stress relaxation tests were carried out on deep low liquid limit clay from an overburden layer, and the stress relaxation characteristics of the clay under different confining pressures were studied. It was found that the initial volume change was rapid under different confining pressures, but the overall volume change was small. The stress relaxation property of the clay decreased significantly with the increase of the confining pressures. In the coordinate system with time on the logarithmic axis, the initial section of the stress relaxation curves under different confining pressures did not follow a linear relationship, but did after a certain period of time. The empirical formulae for the stress relaxation proposed by Lacerda and Houston was further extended based on the test results. A new parameter Q was introduced and defined as the stress relaxation rate, and it was found that the stress relaxation rate Q under different confining pressures decreased rapidly with time and then gradually tended to be stable. Based on this, an empirical equation associated with the stress relaxation rate, confining pressure and time is established, which reveals the law of stress relaxation with time. Based on the volume change results, the relationship of volume change with confining pressure and time under stress relaxation conditions is established, which provides a basis for the generalization and establishment of relevant rheological models.