The National Taiwan University/Purdue (NTU/PU) nonhydrostatic model is used to study mountain waves, hydraulic jumps, and lee vortices. The NTU/PU model is based on a compressible and three-dimensional system of equations with a terrain-following vertical coordinate. A major advantage of the model is the use of a modified forward-backward integration scheme that retains internal gravity waves but suppresses unwanted sound waves. In flow around an isolated ideal elliptical mountain, the simulated flow from the NTU/PU model spreads broadly in the crosswind direction with a well-defined stagnation point at the windward side of the mountain. Two semi-idealized downslope wind cases were conducted using the real topography at White Sand Missile Range (WSMR), New Mexico, USA. Our simulated flows including hydraulic jumps and vortex shedding in the lee of the Organ Mountains agree very well with observations for the case on 25 January 2004, at 15 UTC, but the discrepancy is somewhat larger for the case on 19 January 2004, at 15 UTC. This paper shows that the model results are sensitive to the detailed numerical schemes, filters, and physics, etc. It also suggests that more observations and improvements are required for a model to realistically simulate the flow over complex terrain.