A proper representation of the air flow in a ventilation duct is crucial for adequate prediction of the deposition velocity of particles. In this paper, the mean turbulent air flow fields are predicted by two different numerical models (the Reynolds stress transport model (RSM) and the realizable k-e model). Contours of mean streamwise velocity deduced from the k-e model are compared with those obtained from the Reynolds stress transport model. Dimensionless deposition velocities of particles in downward and upward ventilation duct flows are also compared based on the flow fields presented by the two different numerical models. Trajectories of the particles are tracked using a one way coupling Lagrangian eddy-particle interaction model. Thousands of individual particles are released in the represented flow, and dimensionless deposition velocities are evaluated for the vertical walls in fully developed smooth vertical downward and upward square duct flows generated by the RSM and realizable k-e model. The effects of particle diameter, dimensionless relaxation time, flow direction and air speed in vertical upward and downward square duct flows on the particle deposition velocities are discussed. The effects of lift and gravity on the particle deposition velocities are evaluated in vertical flows presented by the RSM. It is shown that the particle deposition velocities based on the RSM and realizable k-e model have subtle differences. The flow direction and the lift force significantly affect the particle deposition velocities in vertical duct flows. The simulation results are compared with earlier experimental data and the numerical results for fully developed duct flows. It is shown that the deposition velocities predicted are in agreement with the experimental data and the numerical results.