To date, many studies have proposed theories to model the load-induced behavior of sands which have been verified, to some extent, by classical experiments. Theories that can capture the typical stress-strain relationship of sands were then transferred into numerical softwares used in the solution of many geotechnical engineering problems. Without ever moving on from this goal, new models are still being developed, and the progress that has been made thus far now focuses more on how to integrate relevant numerical formulations in the most effective manner or to model the broadest range of soil behavior with fewer model parameters. In this study, the static and dynamic constitutive behaviors of saturated sands are modeled. Within the scope of the Generalized Plasticity Theory, analyses conducted by using a flow and a potential surface in the model are compared with the results obtained without any reference to a surface definition. The need for including such surface functions, which distinguishes the elastic behavior from that of the plastic behavior of sands and which are used to calculate plastic deformations, is questioned here. In this research, firstly the unit vectors for loading and plastic flow directions are defined and the static and dynamic behaviors of sands are calculated. Then, yield and potential surfaces are derived by integrating these unit vectors and the constitutive relations of sand are presented comparatively for the two formulations in terms of a number of triaxial test simulations. In the second part of the study, a new hardening law is proposed to be utilized within the formulation with the surface definitions. The plastic loading modulus is also updated with a newly proposed kinematic interpolation rule and the liquefaction behavior of loose sands is remodeled by subsequently verifying with the available static and dynamic triaxial tests.