A numerical simulation method has been developed to predict atmospheric flow and stack gas diffusion using a calculation domain of several km around a stack under complex terrain conditions containing buildings. The turbulence closure technique using a modified k-$varepsilon$-type model under a non hydrostatic assumption was used for the flow calculation, and some of the calculation grids near the ground were treated as buildings using a terrain-following coordinate system. Stack gas diffusion was predicted using the Lagrangian particle model, that is, the stack gas was represented by the trajectories of released particles. The numerical model was applied separately to the flow and stack gas diffusion around a cubical building and to a two-dimensional ridge in this study, before being applied to an actual terrain containing buildings in our next study. The calculated flow and stack gas diffusion results were compared with those obtained by wind tunnel experiments, and the features of flow and stack gas diffusion, such as the increase in turbulent kinetic energy and the plume spreads of the stack gas behind the building and ridge, were reproduced by both calculations and wind tunnel experiments. Furthermore, the calculated profiles of the mean velocity, turbulent kinetic energy and concentration of the stack gas around the cubical building and the ridge showed good agreement with those of wind tunnel experiments.