The theoretical basis, physical structure, and preliminary evaluation of the U.S. Environmental Protection Agency's Complex Terrain Dispersion Model (CTDM) are described. CTDM is a point-source plume model designed primarily to estimate windward-side surface concentrations on distinct terrain features during stably-stratified flow. The model is based on steady-state, Gaussian diffusion assumptions. Potential flow theory is the basis of the model mechanisms for accounting for terrain-induced alterations in the flow. The model incorporates the critical dividing streamline height concept to separate the flow capable of surmounting the terrain from that restrained to flow around the terrain. Consideration is given to plume meander, source-induced effects on initial diffusion, and alterations in diffusion rates by flow deformation. Preliminary evaluations of the current version of the model with field tracer data and fluid modeling data show that CTDM can identify maximum concentrations with some success but that further refinements are warranted.