A mesoscale atmospheric forecast model configured in a hybrid isentropic - sigma vertical coordinate and used in the NOAA Rapid Update Cycle (RUC) for operational numerical guidance is presented. The RUC model is the only quasi-isentropic forecast model running operationally in the world and is distinguished from other hybrid isentropic models by its application at fairly high horizontal resolution (10 - 20 km) and a generalized vertical coordinate formulation that allows model levels to remain continuous and yet be purely isentropic well into the middle and even lower troposphere. The RUC model is fully described in its 2003 operational version, including numerics and physical parameterizations. The use of these parameterizations, including mixed-phase cloud microphysics and an ensemble-closure-based cumulus parameterization, is fully consistent with the RUC vertical coordinate without any loss of generality. A series of experiments confirm that the RUC hybrid theta-sigma coordinate reduces cross-coordinate transport over a quasi-horizontal sigma coordinate. This reduction in cross-coordinate vertical transport results in less numerical vertical diffusion and thereby improves numerical accuracy for moist reversible processes. Finally, a forecast is presented of a strong cyclogenesis case over the eastern United States in which the RUC model produced an accurate 36-h prediction, especially in a 10-km nested version. Horizontal and vertical plots from these forecasts give evidence of detailed yet coherent structures of potential vorticity, moisture, and vertical motion.