We investigate effects of electron-electron interactions on the shape of the Fermi surface in an anisotropic two-dimensional electron gas using the "RPA-GW" self-energy approximation. We find that the interacting Fermi surface deviates from an ellipse but not in an arbitrary way. The interacting Fermi surface has only two qualitatively distinct shapes for most values of r(s). The Fermi surface undergoes two distinct transitions between these two shapes as r(s) increases. For larger r(s), the degree of the deviation from an ellipse rapidly increases, but, in general, our theory provides a justification for the widely used elliptical Fermi-surface approximation, even for the interacting system, since the nonelliptic corrections are quantitatively rather small except for very large r(s).