A simple mathematical model of fluid flow is applied to determine the cross-sectional shape of a coaxial ground heat exchanger (CGHE) for which the friction pressure drop is minimal. Both laminar and turbulent flows of a Newtonian fluid are analyzed. The dimensionless form of the friction pressure losses is taken as the objective function, and the dimensionless internal diameter and wall thickness of the inner tube is adopted as decision variables, with the reference length taken to be the internal diameter of the external pipe. The resulting optimization problem is solved by means of a hybrid analytical-numerical method. The obtained solutions are generalized as two simple equations valid for laminar and turbulent flows, respectively. It is shown that the pressure losses in a coaxial ground heat exchanger with optimal cross section may be considerably smaller than the pressure losses for a nonoptimal one. The obtained results are significant for the global optimization of CGHEs, resulting in improved energy conservation of buildings and district heating systems.