After the destructive event of December 26, 2004, many attempts have been made to accurately simulate the generation and propagation of tsunami waves in the Indian Ocean. In support of the Tsunami Early Warning System for the Indian Ocean, a very high-resolution finite element model (TsunAWI) has been developed for simulations of the wave propagation. It offers geometrical flexibility by working on unstructured triangular grids and is based on finite-element discretization. The paper presents a brief description of the model, with a focus on its verification and validation. The key issue in modelling the tsunami is wetting and drying. The original algorithm to solve this problem is discussed. Full and reduced formulation of the momentum advection for elements and parameterization of horizontal diffusion are presented. Using the well-known Okushiri test case, the influence of nonlinearity on the wave propagation is demonstrated. Numerical experiments simulating the Indian Ocean Tsunami on December 26, 2004 have been conducted. For the whole Indian Ocean, the comparison of simulation results with observational (coast gauge) data is carried out. A typical tsunami wave is much shorter than tidal waves which are usually neglected in tsunami modelling. However, in coastal areas with strong tidal activity, dynamic nonlinear interaction of tidal and tsunami waves can amplify the magnitude of inundation. To study this effect, water level change due to tide is included in the general scheme. © 2011 Springer-Verlag Berlin Heidelberg.