The correct representation of the failure of geomaterials that feature strength anisotropy and polyaxiality is crucial for many applications. In this contribution, we propose and evaluate through a comparative study a generalized framework that covers both features. Polyaxiality of strength is modeled with a modified Van Eekelen approach, while the anisotropy is modeled using a fabric tensor approach of the Pietruszczak and Mroz type. Both approaches share the same philosophy as they can be applied to simpler failure surfaces, allowing great flexibility in model formulation. The new failure surface is tested against experimental data and its performance compared against classical failure criteria commonly used in geomechanics. Our study finds that the global error between predictions and data is generally smaller for the proposed framework compared to other classical approaches.