Atrial fibrillation (AF) is the most common sustained arrhythmia in the developed world, affecting approximately 1.5% of its population [1]. Although AF is a common arrhythmia its genesis is not well understood. Biophysically detailed computer models of the atria provide a powerful alternative to experimental animal models that allow for in-depth investigations into the roles of specific elements such as ion channel or structural remodelling in arrhythmogenesis. The aim of this study was to develop a 3D mathematical model for the sheep atria. Based on experimental data from Ehrlich et al., Burashnikov et al., and Lenaerts et al. [3-5], electrophysiologically detailed models were developed for different cell types of the sheep atria – the pectinate muscles (PM), crista terminalis (CT), right atrial appendage (RAA), Bachmann’s bundle (BB), the left atrium (LA) and the pulmonary veins (PV). These single cell models were then incorporated into an anatomically detailed reconstruction of a sheep atria, which was segmented into the various cell types and contained detailed fibre orientation information throughout the tissue. Using the developed model, we investigate the genesis of AF, and the importance of electrical heterogeneity and fibre structure on its development. In simulations, fibrillation was induced by rapidly pacing the pulmonary vein region. It was found that AF can be induced when the electrical heterogeneity is modelled, regardless of whether or not the complex fibre structure is considered. However, when the fibre structure was ignored the fibrillatory patterns were very different, with fewer re-entrant wavelets forming and a more homogeneous pattern throughout the atria. When the electrical heterogeneity was ignored it was not possible to induce AF with the same pacing protocol. In conclusion, a biophysically detailed 3D anatomical and electrophysiological model for the sheep atria has been developed, providing a useful tool for studying cardiac arrhythmias such as AF. Our simulation data has shown that the differences in action potential morphology in the atria are key for the genesis of AF, and the complex fibre structure is important for its development.