Underwater landslides are a common source of tsunamis in coastal areas. Theoretical and experimental studies on this problem, however, are scarce because of the difficulties in modeling and observing a submarine slide and the associated tsunami. To study this problem, we present a numerical model that simulates the coupling of a Bingham plastic mudslide on a gentle uniform slope with the surface waves which it generates. A formulation of the dynamics of the problem is presented, where the landslide is treated as an incompressible Bingham plastic flow and the water motion is assumed irrotational. The long-wave approximation is adopted for both water waves and the mudslide. Dispersion of waves and potential turbulent mixing are not considered. The resulting differential equations are solved by a finite difference method. We present the numerical results for successive profiles of the mud surface, the horizontal velocity distributions of the slide, the evolution of the surface elevations, and the distributions of the particle velocity of the water motion. Three major parameters dominate the magnitude of the waves (if the volume of the mud is fixed): the density of mud, the yield stress of the mud, and the depth of water at the mudslide site. Because of the yield stress, the slides stop on the slope when the shear stress exerted on the bottom become smaller than the yield stress. The Bingham plastic behavior of the mud significantly reduces the extent and the speed of the mudslide and also the magnitude of the surface waves generated. Comparison of the solution of the Bingham plastic mudslide model with a snow flow test is presented. The solution of a viscous fluid model has been derived as a special case of the present solution. ¿ American Geophysical Union 1993