Sheep is an animal model often used for experimental studies into the underlying mechanisms of cardiac arrhythmias. Previous studies have shown that biophysically detailed computer models of the heart provide a powerful alternative to experimental animal models for underpinning such mechanisms. In this study we have developed a family of mathematical models for the electrical action potentials of various sheep atrial cell types. We have also developed a 3D model for the anatomical structure of the sheep atria. By incorporating the single cell models into the anatomical structure, a novel computational model for the sheep atria has been reconstructed. This model was then used to investigate the mechanisms by which rapid focal activity in the pulmonary veins can transit to atrial fibrillation. It was found that the anisotropic property of the atria arising from the fibre structure plays an important role in facilitating fibrillatory atrial excitation waves.