Optical system modeling is particularly important for simulation of laser beam propagation over large distances. Ground-satellite-ground propagation is such a system; it includes three stages: the beam preconditioning stage to ready it for propagation over large distances, beam interception at a relay mirror, (possibly including additional beam conditioning), and beam propagation to and detection at a ground-based target board. The target board is designed to measure the efficiency of power transfer in this experiment by integrating over the resulting redistribution of the laser power density. Key elements of the model are the ground-based laser; adaptive optics for aberration correction and correction of atmospheric effects; beam expander; propagation through a turbulent atmosphere; one or more space-based relay mirrors; and downward propagation to a ground-based target board. Laser beam propagation over large distances is best done above the atmosphere to reduce the effects of atmospheric turbulence on the phase of the laser beam. This paper describes the optical modeling of the propagation of a laser beam between two points on the surface of the Earth, using relay mirrors on one or more satellites. Because of the importance of the atmospheric and propagation effects, computer modeling is necessary to develop understanding of the first order design parameters. Some of the important design parameters are characterization of the adaptive mirror for the atmospheric aberration correction, size of the beam expander, apertures of the relay mirror, and acceptable levels of jitter. An example of a propagating laser beam is presented, demonstrating the fully three-dimensional nature of this model.