In this thesis, the fatigue response of arteries to four specific physiological conditions representative of various morphological changes that artery undergo during its lifetime, was explored. Single layered nonlinear elastic micromechanical model of artery was developed for this purpose. A comparative study was completed on fatigue response, in the form of available life and shear stress accumulation, between hypertensive and normotensive arteries. The effects of morphological changes of ageing arteries on the fatigue response of the artery were studied. Change in stiffness, arterial dilation and remodeling were taken into consideration. The effect of undulation of the artery, due to weakening of arterial walls with age or hypertension, on fatigue response, is the third aspect of this study. Lastly, the contribution of the surrounding linear elastic tissue material on fatigue response of the artery was investigated to reflect the in-vivo condition of artery where it is always surrounded by different tissues.