A density- and stress-dependent elasto-plastic model for saturated sands undergoing monotonic undrained torsional shear loading is presented in this paper. The model is developed under an extended general hyperbolic equation (GHE) approach, in which the void ratio and stress level dependence upon stress-strain response of sand is incorporated. Most importantly, a state-dependent stress-dilatancy relationship is introduced to account for the effect of density on the stress ratio. Such a stress-dilatancy relation is used for modeling the excess pore water pressure generation in undrained shear conditions as the mirror effect of volumetric change in drained shear conditions. In this paper, details of the model formulation and soil parameters calibration are described. By using the proposed model, numerical simulation of monotonic undrained torsional shear tests have been carried out on Toyoura sand. The model predictions show that undrained shear behavior, described in terms of stress-strain relationship and effective stress path for both loose and dense sands can be modeled satisfactorily by using a single set of soil parameters.