In this thesis, a reduced-order model is constructed to study the physiological flow and wall shear stress conditions for aneurysms. The method of local proper orthogonal decomposition (POD) is used to construct the reduced-order modes using a series of CFD results, which are subsequently improved using a QR-factorization technique to satisfy the various boundary conditions in physiological flow problems. This method can effectively construct a computationally efficient physiological model, which allows us to examine the fluid velocities and wall shear stress distributions over a range of different physiological flow parameters. Aneurysms are the dilation, bulging, or ballooning-out of part of the wall of a human artery. Repetitive forces on an existing aneurysm can lead either to its gradual expansion or to a devastating event of rupture. Traditionally, clinicians use the largest diameter as the sole parameter for standard risk stratification outside of clinical trials. However, there seems to be no safe small aneurysm size and a more accurate answer depends on the exact distributions of material and geometrical properties of the aneurysms. Aneurysms can have a very non-uniform distribution of thickness, modulus, and failure tension. We focus on the thins-shell fluid-structures interactions (FSI) with thickness inhomogeneity by studying the influence of one or multiple thin spots on the flow-induced instabilities of flexile shells of revolution with non-zero Gaussian curvatures. The results show that for shells with positive Gaussian curvatures conveying fluid, the existence of a thin spot results in a localized flow-induced buckling response of the shell in the neighborhood of the thin spot, and significantly reduces the critical flow velocity for buckling instability. For shells with negative Gaussian curvatures, the buckling response is extended along the shell’s characteristic lines and the critical flow velocity is only slightly reduced. Finally, the shell model with non-uniform thickness is combined with the ROM of hemodynamic loads. We show that based on a growth and remodeling (G&R) model, the rate of aneurysmal wall’s elastin degradation can be predicted efficiently with various degrees of thickness inhomogeneity.