The present paper investigated the capability of various non-linear k–ε models for predicting flow field and pollutant dispersion around a cubical model building with a stack vent located on its roof center within the turbulent boundary layer. One quadratic model proposed by Nisizima and Yoshizawa, and two cubic models, proposed by Lien et al. and Ehrhard and Moussiopoulos were examined by comparing their simulation results with the wind tunnel data and standard k–ε model. All the computations were performed by using the self-developed object-oriented C++ programming in OpenFOAM CFD package, which contains applications and utilities for finite volume solvers. The standard k–ε model provided inadequate results for the flow field, because it could not reproduce the basic flow structures, such as reverse flow on the roof. By contrast, the non-linear models were able to predict anisotropic stresses and correctly showed the dominant stress over the roof to be the streamwise Reynolds stress. The non-linear models were able to predict the concentration field better than the SKE model due to inclusion of the quadratic and cubic terms. Among the RANS models, the Ehrhard model showed the best agreement with the experimental data. It was shown that concentrations predicted by all turbulence models were less diffusive than those of the experiment, although the non-linear k–ε models have reduced this difference.