The present article is devoted to the influence of sediment layers on the process of tsunami generation. The main scope here is to demonstrate and especially quantify the effect of sedimentation on seabed vertical displacements due to an underwater earthquake. The fault is modelled as a Volterra-type dislocation in an elastic half-space. The elastodynamics equations are integrated with a finite element method. A comparison between two cases is performed. The first one corresponds to the classical situation of an elastic homogeneous and isotropic half-space, which is traditionally used for the generation of tsunamis. The second test case takes into account the presence of a sediment layer separating the oceanic column from the hard rock. Some important differences are revealed. The results of the present study may partially explain why the great Sumatra-Andaman earthquake of 26 December 2004 produced such a big tsunami. More precisely, we conjecture that the wave amplitude in the generation region may have been amplified by important sedimentary deposits in the Indonesian basin. In this study we shed light on the mechanism of amplification through careful numerical simulations.