The numerical tsunami model NAMI-DANCE solving the equations of the nonlinear-dispersive theory of long waves is described. It is developed in cooperation of Turkish and Russian specialists and has been used to simulate tsunami characteristics since 2003. The basic model solver simulates the wave propagation with the well-known nonlinear shallow-water equations. The numerical scheme is based on the Leap-Frog method. The long wave dispersion related to the finiteness of water depth is modeled with the help of numerical dispersion by using specific conditions for spatial and temporal steps. The equations are solved in spherical (geographical) coordinates on rotated Earth taking into account nonlinear quadratic friction in the near-bottom layer. The NAMI-DANCE model is adapted to simulate the generation and propagation of tsunamis of various origin from: underwater earthquakes, submarine landslides, and meteo-tsunamis. For the seismic origin tsunami waves, the initial conditions for hydrodynamic equations are found from the Okada solution; the model allows simulating several sources from different fault segments in the earthquake zone. In the case of the meteo-tsunami, the spatial and temporal distribution of the atmospheric pressure is used as external force. The process of generating the landslide origin tsunami waves, is analyzed in the framework of the two-layer model with a lower viscous layer modeling the submarine landslide motion and an upper layer is the water body. The boundary conditions on the open boundaries correspond to the free-wave passage. The run-up process is also computed using the bathymetry and topography at the coastal boundaries. The NAMI- DANCE code has been verified with several benchmarks according to the NTHMP benchmarks. The difficulties of tsunami modelling connected with the lack of accuracy in the bottom bathymetry and the land topography are mentioned. The use of the developed code for the tsunami action analysis on the coasts and constructions is demonstrated.