Inhaled asbestos fibres have been implicated in causal relationships with increased frequencies of non-malignant pleural disease, asbestosis, mesothelioma and lung cancer. Replacement fibres are considered to be less harmful, however, their health effects are not fully understood. The objective of the present work was to implement and apply numerical fibre tracking techniques in order to simulate the deposition of fibres in a complex oro-pharyngeal-laryngeal-bronchial system at different inhalation flow rates and compare the results with the outcomes of recent measurements performed in the same geometry. Two different approaches for the estimation of drag force were considered. Simulated deposition efficiency values agreed reasonably well with the experimentally determined values, however, the drag model which considers the anisotropic nature of the geometry of fibres performed better than the one which accounted only for the their non-spherical shape. The highest values of deposition density correlated well with the location of primary lesions observed in pathological studies.