Ray acoustics has been applied to the propagation of sound waves in a homogeneous moving medium with sheared flow bounded by the hard walls of a duct. Differential equations describing the ray trajectories and spreading losses along each ray were developed and solved numerically for a range of centerline Mach numbers and shear boundary-layers. Results were obtained which show the effects of upstream and downstream sound propagation on the ray paths. A method was also presented which allows the calculation of intensity loss profiles at specified cross-sections of the duct.