A steady stream of concentrated granular suspension (mud) is introduced at a fixed location on a sloping plane, and flows downslope under gravity. As it does so, it spreads laterally and becomes thinner. This flow is of considerable geophysical interest. The theoretical analysis is based on a natural approximation of thin film or lubrication-theory type. First, the requirements of this theory are carefully examined and the conditions necessary for its validity are made explicit. Then the governing equations are solved numerically. A comparison is made with experimental data (and with theory) reported previously. It is shown that the theory is inapplicable in some cases, somewhat contrary to expectation; however, good agreement is obtained in others.