Numerical experiments are conducted for two-dimensional model problems of tsunami generation by underwater slides and slumps. These problems consist of a semi-ellipse, translating down an incline with a prescribed center of mass motion. For each problem, this motion is derived as a function of geometric and material parameters, and we calculate corresponding characteristic tsunami amplitudes. Landslide deformation is shown to have negligible effect on these amplitudes. Results of numerical experiments for the model problems are converted into predictive curve fits of characteristic tsunami amplitudes as functions of nondimensional governing parameters. Such results are useful for estimating tsunami hazard or for performing case studies. A method is proposed to input free surface displacements, modeled shortly after tsunami generation, into tsunami propagation models, in essence treating such submarine mass failures exactly like coseismic displacement.