In this article the capabilities or mathematical heavy gas atmospheric dispersion models to describe the dispersion or heavy gases in complex and obstructed terrain arc presented. The models have been entegorizcd into three main classes: phenomenological (empirical) models. intermediate (engineering) models and computational fluid dynamic (research) models. Each group or models is discussed separately. The general features or the models arc discussed briefly, Examples of the heavy gas atmospheric dispersion models carable to treat the influence or non-Ilut and obstructed terrain on the heavy gas dispersion result from the work carried out in the European Union and in the US. No model simulating the heavy gas atmospheric dispersion over complex or obstructed terrain has been yet developed in Poland. The need lor future work on the effects of complex and obstructed terrain on the heavy gas atmospheric dispersion is expressed. future research in the area should include both experimental and modeling work. In the context of this raper future modeling work is worth considering in more detail. il seems that all the approaches 10 describe the hcavv gas atmospheric dispersion over complex and obstructed terrain arc worth further aucntion. This opinion is supported by the fact that these approaches arc used in different types of heavy gas dispersion models. which in turn differ in applications. The simpler methods arc introduced to the simpler heavy gas atmospheric dispersion models applied mainly in the routine calculations. The advanced techniques capable to describe the: now near complicated geometrics are used in the sophisticated models applied mainly as a research tools.