In this work, utilizing the result of the experiment that we conducted on a dog's upper thoracic aorta, a two layered cylindrical shell model is presented. A series of bi-axial tests were carried out on the specimens taken from the media and adventitia of an aortic segment and the stress-stretch relations were obtained. Considering the morphological structures of media and adventitia, an orthotropic elastic model for media and an isotropic elastic model for adventitia is presented. By comparing theoretical results and experimental measurements, the values of material constants appearing in the model have been determined. Finally, using the elastic models introduced, the inflation and axial extension of a layered cylindrical aorta was studied.