We study the effects of an elliptical Fermi surface deformation on the energy of a two-dimensional electron gas. We consider a standard model for fully spin-polarized (spinless) electrons embedded in a uniformly charged neutralizing jellium background and treat the system in the thermodynamic (bulk) limit. We calculate exactly the energy changes of the system as a function of a parameter that gauges the elliptic deformation of the Fermi surface. The results obtained give insight on various scenarios and competing tendencies that may arise in such a system in presence of some form of internal anisotropy originating from factors such as electron's anisotropic effective mass, anisotropic interaction potential or both.