New excavation or tunnelling affects the stress state of soils in ground. The change of stress state due to excavation may affect the cyclic behaviour of soils. Cyclic loading, such as traffic and earthquake loading, induced ground deformation may be greater than expected if such effect is not considered. A series of cyclic triaxial tests were performed on Sydney sand with different relative densities. The effect of unloading sequence on deformation of the sand under cyclic loading was simulated by reducing lateral stress in steps between loading cycles. The dependence of strain accumulation on the magnitude of confining pressure reduction and on unloading stress paths was studied. The results indicate that the sand has a memory of stress history and the stress history of such unloading enlarges the strain accumulation during the subsequent cycles, and the greater the reduction of lateral stress, the greater the accumulated strain. Under cyclic loading, the accumulated axial strain could increase nonlinearly or linearly with the ratio of unloading magnitude to initial mean effective stress, depending on the stress state before cyclic loading. The unloading stress paths have limited effects on the final accumulated strain if the initial and final stress states are the same. The variation of strain accumulation direction attributes to the change of average stress ratio resulting from lateral stress reduction, but hardly depends on relative density and unloading stress paths. The strain accumulation direction after unloading roughly agrees with the modified Cam Clay flow rule.