Health hazards associated with inhalation of toxic particles depend on the extent of exposure. Thus, knowledge of transport and deposition properties of aerosol particles in lung flows is essential. Spherical particles may potentially cause adverse health effects when inhaled, and fibers may cause additional harm due to their specific shape. Asbestos is a well-known example of hazardous fibrous materials, and more recently this has also called for concern on the extended use of nanotubes. A numerical model is developed for transport and deposition of fibrous particles in the respiratory airways. Fibers are represented by prolate spheroids, and expressions from Jeffery(1922) are used for the fluid dynamic torque. Transport of non-spherical particles includes both translational and rotational motion. In the past, Euler angles have frequently been used to describe the resulting fiber orientation, but the Euler angles bring problems with singular terms for certain angles and thus are not suited for rigid motion simulations for fibers undergoing full rotations. Here, the evolvement of fiber orientation with time is calculated with quaternions, which have well-behaved equations of motion. The model is valid for arbitrary Stokes flows at low particle concentrations. Forces included are fluid dynamic drag, gravity and Brownian diffusion, making the model applicable for fibers with diameters ranging from nano- to microscale. Results so far show that fibers with larger aspect ratios are transported further before being deposited on the airway walls. This implies that the potential for a fiber to reach the distal airways increases with increased fiber aspect ratio, regardless of particle size.