In order to predict complex transient debris flows we developed a numerical model based on shallow-water-equations. We consider only muddy debris flows whose behaviour is well described by a Herschel-Bulkley model. In laminar regime, the wall friction force is assumed to be equal to the resistance of a steady uniform flow having same depth and mean velocity. The model parameters, directly deduced from the fluid behaviour, are determined independently by rheometrical measurements. The main characteristics of our experimental transient flows, established in a laboratory flume, are in fairly good agreement with the predictions of the numerical model. It should be noticed that these results were obtained without any complementary fitting.