With the advent of ever faster computers, the operational use of nonhydrostatic atmospheric models at resolutions beyond the hydrostatic limit has become a reality. A renewed global research effort is being made to formulate and improve nonhydrostatic models. In this paper, the status of numerical atmospheric modeling research in South Africa is briefly reviewed. We then report on the development of a new, nonhydrostatic atmospheric model at the University of Pretoria. The dynamic kernel of the model is based on a novel, split semi-Lagrangian formulation of a set of quasi-elastic equations in a terrain-following vertical coordinate based on the full pressure field. The main features of the model dynamics and numerics are discussed, and it is noted that the governing equation set presented here has not been applied in atmospheric modeling before. The model may be used to perform state-of-the-art research in numerical model development, for instance, for the derivation of new equation sets, numerical techniques and vertical coordinate systems. The model's ability to simulate highly nonlinear and nonhydrostatic flow is illustrated by means of a convective bubble experiment, where an updraft interacts with vertical shear of the horizontal wind. This experiment illustrates the potential of the new model to be used in the study of thunderstorm dynamics.