A particle model LAMDA suitable for dealing with the atmospheric dispersion is presented. The reliability of the model is tested comparing the results of its simulations to the wind tunnel measurements by Khurshudyanet al. (1981). Two versions of the model, both based on the Langevin equation and askewed distribution of the vertical wind velocity fluctuations, are considered. To develop the second version of the model we derived a proper scheme to produce skewed distributions of particle velocities consistent with the observed first and second moments of turbulent fluctuating velocities, with their horizontal and vertical derivatives, and their cross-correlations. The 2D geometry of the obstacle (in the wind tunnel experiment considered) allowed some simplifications. Due to the lack of some input data (such as the vertical profiles of crosswind standard deviation of wind velocity fluctuations and of the Lagrangian time scales) we looked for three different parametrizations. It was found that particular combinations of measured and parametrized data could give rise to critical vertical regions in which the derived scheme for the generation of random vertical velocity fluctuations cannot be applied. The best vertical distributions of the Lagrangian time scales (third parametrization) were estimated by fitting simple formulations for the average plume height and lateral variances to the measured data. The main results of this work were the model performance in simulating dispersion in shear flow over flat terrain, and its sensivity to the shape of the crosscorrelation term\(\overline {u'w'} \).