In the framework of this dissertation, the nonhydrostatic tsunami simulation model TsunAWI-NH was developed as a modular extension of the hydrostatic shallow water model TsunAWI by accounting for terms that are neglected in the hydrostatic approach. Applied on test cases depending on tank experiments, the comparison of hydrostatic and nonhydrostatic model results shows a significant improvement by using TsunAWI-NH. However, in each time step, a system of linear equations has to be solved. That results in a long computing time and an increased demand for memory resources. Several numerical techniques are investigated, e.g., sequential and parallel preconditioning methods applied to the Krylov subspace method FGMRES(m), domain decomposition techniques and resorting algorithms. A sophisticated implementation enables TsunAWI-NH to simulate complex tsunami scenarios. For some real tsunami events, the model results of TsunAWI-NH and TsunAWI are compared with observation data.