Heat transfer by pile and borehole ground heat exchangers involves transient heat conduction in composite media together with complex geometry. To meet this engineering challenge, this paper presents a modeling approach based on composite-medium line-source solutions. The central idea of this new model is that the downward and upward channels of U-shaped tubes (not the borehole) are approximated as line sources or sinks of heat placed in a composite medium. A two-dimensional finite volume model and a reference data set of a sand-box experiment are used to verify and validate the new modeling method. The numerical model uses a novel time-varying boundary condition for the inner walls of U-tube legs and thus can account for effect of heat capacities of circulating water, U-shaped tubes, as well as grouting materials. Comparisons between the analytical and the numerical models are also made for different parameters. To conclude, the new composite medium line-source model can address not only heat capacity of grout but also the property difference between grout and the ground. More importantly, this approach is enough general and flexible to model various configurations of heat transfer channels, including single and double U-shaped, W-shaped channels, spiral-coils, etc.