Particle deposition in the lungs have so far been modeled mainly with the assumption of laminar flow. In the present study, several Reynolds-Averaged Navier-Stokes (RANS) turbulence models are used to simulate the airflow and particle deposition in the human respiratory system. The theory behind RANS turbulence modeling is treated in detail. The simulation results are compared to Large Eddy Simulations (LES) reference data, and it is demonstrated that relatively simple two-equation eddy viscosity models seem adequate to reproduce the primary features of the flow field. The present study seems to suggest that the RANS approach gives realistic results for particles with diameters greater than about 10 micrometers.