As an example of the activity in the field of rapid granular flow, we sketch an analysis of a rapid granular flow of identical frictionless spheres that is driven by gravity down an incline. The flow is assumed to be dense, collisional, steady, and fully developed. Because we employ conditions at the base of the flow that are appropriate for a bumpy, frictionless boundary, the analysis is slightly more complicated than that of Savage (1983a, in Theory of Dispersed Multiphase Flow, RE Meyer (ed), Academic Press, New York, 339-358). Because we restrict our attention to dense flows, it is somewhat simpler than that of Richman and Marciniec (1990, J Appl Mech57 , 1036-1043). It is essentially that of the dense collisional regime considered by Anderson and Jackson (1992, J Fluid Mech241 , 145-168). We outline the determination of the profiles of the mean velocity, fluctuation velocity, and concentration through the depth of the flow and indicate how the boundary conditions provide relations between the depth of the flow, the angle of inclination, the fluctuation velocity at the base of the flow, and the mean velocity at the free surface.