Abstract: The apparatus for static and dynamic universal triaxial and torsional shear tests was employed to perform cyclic torsional shear tests and coupled vertical and torsional shear tests on soil under unconsolidated-undrained conditions.Through a series of tests on saturated clay,the effect of stepped loading history and coupled cyclic stress on dynamic shear modulus and damping ratio under large strain(>10-3) was examined.It was indicated that the stepped loading method could be used to determine the dynamic shear modulus and the damping ratio since the initial backbone curve,dynamic shear modulus and damping ratio obtained from single-step loading tests by use of many clay samples were consistent with those obtained from stepped loading tests by use of one clay sample.There was an obvious effect of cyclic axial deviatoric stress on the obliquity of stress-strain hysteresis loops as well as on the dynamic shear modulus and the damping ratio.Especially under the low cyclic torsional shear stress,the increments of dynamic shear modulus seemed to be controlled by the magnitude of axial deviatoric stress.The variations of axial stress-strain hysteresis loops were complicated due to the influences of cyclic torsional shear stress.