Non-hydrostatic, mesoscale atmospheric models are an essential tool m a wide range of applications which require enhanced forecasting skills. Advanced numerical methods can significantly contribute to a better understanding of these models. This research project is devoted to the numerical analysis and the applications of semi-implicit time discretization and of high-order, conservative and positive numerical schemes to the equations of mesoscale atmospheric models. A semi-implicit mesoscale numerical model will be developed, in which modern conservative numerical schemes are employed. The proposed approach will allow for greater efficiency, by achieving an increase of the discretization time step and a fine vertical resolution. A main area of application will be the study of three dimensional flows over complex orography.