While the benefits and possibilities of nanotechnology have received considerable attention, the adverse health effects that may follow with widespread use have not until recently been illuminated. Recent studies have shown that nanoparticles, due to their smaller size and thereby bigger surface area and surface reactivity, can be more toxic than larger particles of the same material. However, the risks associated with the use of nanoparticles also depend on the extent of exposure. In this thesis, the effects upon inhalation are studied. In vivo and in vitro studies would be very cost-intensive and difficult to perform for the study of particle transport and deposition in the human airways. Therefore, numerical simulations are increasingly being carried out together with validating experiments when possible. The influence of particle size is studied on transport and deposition patterns in a rigid, smooth-walled model of the human airways, extending from trachea to the segmental bronchi. The morphometrical data is based on the asymmetric lung model of Horsfield et al. (1971). Particle deposition efficiency and localisation is compared for particles (density = 1950 kg/m^3) in the size range 0.015-100 micrometres at inspiratory flow rates of 0.1-1.0 l/s, measured at trachea. The commercial Computational Fluid Dynamics (CFD) software package ANSYS CFX 10.0 is used for analysis. A Lagrangian multiphase model approach is employed, and one-way coupling is used between the continuum and dispersed phase, which allows particle tracking to be run as a Post-process. Steady, laminar, 3-dimensional flow is simulated and forces included are drag and gravity. The sizes of systematic errors are estimated, allowing analysis of accuracy of the results. Particle size has substantial influence on deposition, regarding both efficiency and localisation. Deposition mainly occurs by inertial impaction, and gravity can be neglected at higher flow rates. Deposition generally increases with increase in particle size and flow rate. The major part of the larger microparticles are captured at the first bifurcation, while smaller microparticles are deposited less efficient, but more uniformly throughout the model. The nanoparticles essentially follow the streamlines through the model, and only a few percent are deposited in the region modelled. Deposition patterns are affected by geometrical asymmetry, and local deposition fractions differ up to 25 % between bifurcation units of the same generation.