Distribution patterns of odorant molecules in the rat nasal olfactory region depend in large part on the detailed airflow patterns in the nasal cavity, which in turn depend on the anatomical structure. To investigate these flow patterns, we constructed an anatomically accurate finite element model of the right nasal cavity of the Sprague-Dawley rat based on horizontal (anterior-posterior) nasal cast cross sections. By numerically solving the fluid mechanical momentum and continuity equations using the finite element method, we studied the flow distribution and the complete velocity field for both inspiration and expiration throughout the nasal cavity under physiological flow rates of resting breathing and sniffing. Detailed velocity profiles, volumetric flow distributions, and streamline patterns for quasi-steady airflow are presented. S-shaped streamlines passing through the olfactory region are found to be less prevalent during expiratory than inspiratory flow leading to trapping and an increase in odorant molecule retention in the olfactory region during sniffing. The rat nasal velocity calculations will be used to study the distribution of odorant uptake onto the rat olfactory mucosa and compare it with the known anatomic location of some types of rat olfactory receptors.