We analyze the influence of hyperelasticity on the plastic behavior of materials. A specific class of what we call hyperbolic elasticity arises from theoretical considerations as straight consequence of plastic invariance of elastic domain. The latter property of fixed residual plasticity is observed experimentally for many geomaterials. We superimpose hyperelastic effects on the plastic Drucker-Prager constitutive relation, widely used in geoscience. Curiously, we found that the hyperbolic nonlinearity, introduced through the Standard Generalized Material formalism, curves the initially linear surface to a quadratic one, that is assimilated to the generalized Hoek-Brown criterion. We conclude than that one possible justification of the empirical Hoek-Brown fit is the material's hyperlastic nature.