Vascular smooth muscle cells (VSMCs) are subject to interstitial flow-induced shear stress, which is a critical parameter in cardiovascular disease progression. Transmural pressure loading and residual stresses alter the hydraulic conductivity of the arterial layers and modulate the interstitial fluid flux through the arterial wall. In this paper, a biphasic multilayer model of a common carotid artery (CCA) with anisotropic fiber-reinforced soft tissue and strain-dependent permeability is developed in FEBio software. After the verification of the numerical predictions, age-related arterial thickening and stiffening effects on arterial deformation and interstitial flow are computed under physiological geometry and physical parameters. We found that circumferential residual stress shifts outward in each layer and its gradient increases up to 6 times with aging. Internally pressurized CCA displays nonlinear deformation. In the aged artery, the circumferential stress becomes greater on the media layer (82-158kPa) and lower on the intima and adventitia (19-23kPa and 25-28kPa, respectively). The radial compression of the intima reduces the total hydraulic conductivity by 48% in the young and 16% in the aged arterial walls. Consequently, the average radial interstitial flux increases with pressure by 14% in the young and 91% in the aged arteries. Accordingly, the flow shear stress experienced by the VSMCs becomes more significant for aged arteries, which may accelerate cardiovascular disease progression compared to young arteries.