The generalized bounding surface model (GBSM) is a fully three-dimensional, time-dependent model for saturated cohesive soils that accounts for both inherent and stress-induced anisotropy, as well as strain softening and the effect of temperature on the material response. The GBSM combines many previous bounding surface models for saturated cohesive soils and enhances their predictive capabilities. In this paper, certain restrictions that are placed on the analytical definition of the bounding surface associated with the GBSM are identified. The manner in which such restrictions manifest themselves and potentially limit the performance of the model are explained. The remedies that have been developed to overcome such shortcomings are described. Numerical simulations and predictions are presented that provide greater insight into different forms of the GBSM as they are used to simulate the drained and undrained response of isotropically and anisotropically consolidated cohesive soils under axisymmetric and true triaxial states of stress.