Abstract: The dilatancy of sands highly depends on the cyclic stress path. A series of axial-torsional coupling shear tests are performed on the Nanjing fine sand under isotropically consolidated condition by using the hollow cyclic apparatus (HCA). The dilatant behavior of saturated sands is investigated under complex stress paths, using the correspondent mathematical model. The results are summarized as follows: the volumetric strain of sands is composed of a completely reversible component and an irreversible component. The cyclic stress path has significant effects on the development of the volumetric strain. The equivalent cyclic stress ratio (ESR), which is defined as the ratio of the mean value of the maximum shear stress in a loading cycle to the initial effective confining pressure, can be used as an index to quantitatively characterize the cyclic stress paths of the soil samples under bi-directional shear loadings. The volumetric strain increment may be uniquely correlated to the applied ESR, which accumulates linearly with the increase of ESR. By introducing ESR, a normalized incremental model for volumetric strain of the saturated sands under bi-directional shear loadings is proposed. Retrospective simulation of a laboratory test using the proposed model shows good agreement, calibrating the reliability of the model. However, the Byrne model based on the data of direct shear tests significantly underestimates the volumetric strain accumulation of the Nanjing fine sand under the axial-torsional coupling shear loadings.