In the last thirty years, both theoretical and experimental investigations supported the analysis of the behavior of dense gases when released in the atmosphere. A few classes of models were developed, differing for the level of detail of the cloud description. For design purposes as well as operator training, we focused on a fast-running model, capable of dealing with complex environments, e.g., chemical facilities and urban areas. Consequently, we opted for the approach based on the shallow water equations, i.e. a system of partial differential equations describing the cloud height, and the spreading velocities in the horizontal directions. The cloud density is inferred from the cloud height and the entrained volume of air. The manuscript discusses the theoretical framework that was implemented to describe thedense gas behavior by means of the shallow water equations.