This paper proposes that elastic potentials, which may be rigorously formulated using the negative Gibbs free energy or the complementary strain energy density, may be used as the yield surface of elasto-plastic constitutive models. Thus, the yield surface may be assumed in some materials as an elastic potential surface for a specific level of critical complementary strain energy density. Traditional approaches, such as the total strain energy criterion, only consider second order terms, i.e., the elastic potential is centred at the origin of the current stress state. Here, first order terms are considered, and consequently, the elastic potential may be translated, which allows to reproduce the desired level of tension-compression asymmetry. The proposed approach only adds two additional parameters, e.g., uniaxial compressive and tensile yield limits, to the elastic ones. For linear elasticity, the proposed approach provides elliptical yield surfaces and shows a correlation between the shape of the ellipse and the Poisson's ratio, which agree with published experimental data for soils and metallic glasses. This elliptical yield surface also fits well experimental values of amorphous polymers and some rocks. Besides, the proposed approach automatically considers the influence of the intermediate stress. For non-linear elasticity, a wider range of elastic potentials, i.e., yield surfaces, are possible, such as distorted ellipsoids. For the case of incompressible non-linear materials, the yield surfaces are between von Mises and Tresca ones.