Conventional yield criteria for ductile materials, such as Tresca and von Mises, predict that yielding is independent on the hydrostatic stress state (pressure), which means that tensile and compressive stress-strain behaviors are considered equal and are equally treated. This approach is reasonable for ductile metallic materials but sometimes inaccurate for polymers, which commonly present larger compressive yield strength, therefore being characterized as uneven. Some pressure dependent theories are available, but there is no consensus concerning the choice of the most appropriate criterion, its use and benefits. As a step in the direction of improving structural integrity practices taking advantage of unevenness, this work performs three key-activities: i) first, a critical review about existing theories and its accuracy; ii) second, a series of experiments under tension and compression including four selected polymers (PA-66, PA-6, PP, and HDPE) to assess real unevenness levels; iii) third, a numerical evaluation of the potential benefits of using modified criteria. Stress states, safety, and stiffness were evaluated for a typical application to illustrate the proposals. Mass reductions up to 39% could be achieved even with simple geometric changes, while keeping original safety and stiffness levels.