Using an accurate numerical method for simulating the advection and diffusion of pollution puffs it is demonstrated that point releases of pollution grow into a shape reflecting the vertical wind shear profile experienced by the puff within a time scale of a less than four hours. For distances beyond several 10s of kilometers from a release point, shear-related dispersion effects are probably the dominant mechanism affecting the area and magnitude of surface impacts. For assessing long-range pollutant dispersion, the common assumption that pollutants disperse as horizontally spherical “puffs” in the atmosphere is inherently inaccurate since shear-induced horizontal spreading of pollution is not a homogeneous “turbulent-like” diffusion process. A Lagrangian puff model can simulate an area impacted by a pollution puff only if larger shear-dependent horizontal puff dispersions are assumed. However, even if impacted areas are reasonably simulated, peak concentrations will be severely underestimated since atmospheric puffs influenced by even small amounts of wind shear are nonspherical. If horizontal dispersion coefficients in a Lagrangian puff model are adjusted so that peak concentrations are correctly simulated, then the calculated pollution impact area will be severely skewed. In shear environments, no choice of horizontal dispersion coefficients in a single-puff Lagrangian model will yield reasonable correlations with puffs that are skewed into nonspherical shapes by atmospheric wind shear.