A key requirement in the assessment of landslide risk in such densely populated urban areas as Hong Kong consists of the prediction of potential runout distance or the extent of the subsequent debris flow. This paper presents a three-dimensional dynamic model of unsteady gravity-driven debris flow. The Lagrangian Galerkin finite element method is used to determine the nodal velocity and depth of soil column elements within the sliding mass, with the momentum and mass conservation mathematically closed within the soil column elements. The numerical solution also features a lumped mass matrix and a volume-weighted procedure. The method of least squares approximation plays a smoothing role which enhances stability and efficiency of the numerical solution scheme. The nodal elevation during sliding is obtained via a dynamic bilinear interpolation of the elevation function for the base of the sliding mass. Furthermore, the accuracy, robustness, and generality of this method are validated by experimental results. Its application to the Shum Wan Road landslide and the Fei Tsui Road landslide, both of which occurred during a heavy rainstorm in Hong Kong on 13 August 1995 and involved fatalities, gives reasonable results in comparison to the field observations. A variety of rheological constitutive relationships have already been coded in the present program to provide flexibility and adaptability in practical applications.Key words: debris flows, three-dimensional dynamic model, runout distance.