In sloped ground, soil elements are subjected to an initial static shear stress on the horizontal plane or an assumed failure surface. During earthquake shaking, these elements are subjected to additional cyclic shear stress due to shear waves propagating vertically upward from bedrock. The superimposition of static and cyclic shear stresses can have major effects on the response of the soil, leading to liquefaction-induced failure behavior of natural and artificial slopes of sandy deposits and the consequent development of extremely large ground deformation. In order to address the above issue, in this paper, a method to assess the failure behavior of sand specimens with initial static shear under undrained cyclic shear loading is presented. Its applicability has been investigated on a wide range of combinations of static and cyclic shear stresses on very loose, loose and dense sand by referring to: (i) the results of undrained cyclic torsional shear tests carried out on saturated Toyoura sand specimens; and (ii) a number of single-element numerical simulations by employing an elasto-plastic constitutive model developed at the Institute of Industrial Science (IIS), University of Tokyo.