Ground source heat pump (GSHP) systems extract heat or cold from the ground by circulating a heat carrier uid (HCF) in a ground heat exchanger and inject this energy in buildings. This paper shows that there exists an optimal HCF ow rate which minimizes the energy use of such systems. The paper proposes an analytical solution for the optimal ow rate as a function of measurable variables, system parameters and data that can easily be derived from manufacturer data sheets. The analytical solution is validated using a detailed simulation model representing an existing GSHP system of 99 boreholes with a depth of 30m.