Although much research considers heavy gas dispersion over flat ground, less is known about the physics of dense gas dispersion on a slope. Here, the appropriateness of shallow layer models for the simple case of releases over a slope in a calm ambient is assessed. This two-part paper assesses the value of shallow layer modelling using the established shallow layer model TWODEE [J. Hazard. Mater. 66 (3) (1999) 211; J. Hazard. Mater. 66 (3) (1999) 227; J. Hazard. Mater. 66 (3) (1999) 239] and the experimental results of Schatzmann et al. [M. Schatzmann, K. Marotzke, J. Donat, Research on continuous and instantaneous heavy gas clouds, contribution of sub-project EV 4T-0021-D to the final report of the joint CEC project, Technical Report, Meteorological Institute, University of Hamburg, February 1991]. Part I considers continuous releases, and part II considers instantaneous releases; both use the same model with the same entrainment coefficients. For continuous releases, cloud arrival times are generally well predicted, and cloud concentrations are generally correct to within a factor of two. Shallow layer models thus appear to be capable of physically accurate simulation of continuous releases over a slope in a calm ambient. (C) 2003 Elsevier B.V. All rights reserved.