The problem of transport of suspended sediment after the break of a dam on an inclined bed is considered. To that end we use the shallow-water approximation for arbitrary, constant slopes of the bottom, taking into consideration the effect of friction. The numerical technique and the frictional model are validated by comparison with available experimental data and asymptotic analytical solutions, with special attention to the numerical solution near the wetting front. The transport of suspended sediment down the inclined bed is obtained and discussed as a function of the slope of the bed for different values of the parameters characterizing the sediment and its transport properties. For sufficiently large times we always find the formation of roll waves near the water front, which affects the transport of sediments significantly. These strong oscillations are accurately computed with the numerical method used. The relative importance of the bed load (to the suspended load) sediment transport is also discussed as a function of the size of the sediment particles and the slope of the bed for different models on the initiation of sediment suspension from bed load. We also check the dilute sediment approach and characterize the conditions for its failure. Finally, the results of the present simplified model are intended to be used as tests of more complex numerical models.