Intimal thickening due to atherosclerotic lesions or intimal hyperplasia in medium to large blood vessels is a major contributor to heart disease, the leading cause of death in the Western World. Balloon angioplasty with stenting, bypass surgery, and endarterectomy (with or without patch reconstruction) are some of the techniques currently applied to occluded blood vessels. On the basis of the preponderance of clinical evidence that disturbed flow patterns play a key role in the onset and progression of atherosclerosis and intimal hyperplasia, it is of interest to analyze suitable hemodynamic wall parameters that indicate susceptible sites of intimal thickening and/or favorable conditions for thrombi formation. These parameters, based on the wall shear stress, wall pressure, or particle deposition, are applied to interpret experimental/clinical observations of intimal thickening. Utilizing the parameters as "indicator" functions, internal branching blood vessel geometries are analyzed and possibly altered for different purposes: early detection of possibly highly stenosed vessel segments, prediction of future disease progression, and vessel redesign to potentially improve long-term patency rates. At the present time, the focus is on the identification of susceptible sites in branching blood vessels and their subsequent redesign, employing hemodynamic wall parameters. Specifically, the time-averaged wall shear stress (WSS), its spatial gradient (WSSG), the oscillatory shear index (OSI), and the wall shear stress angle gradient (WSSAG) are compared with experimental data for an aortoceliac junction. Then, the OSI, wall particle density (WPD), and WSSAG are segmentally averaged for different carotid artery bifurcations and compared with clinical data of intimal thickening. The third branching blood vessel under consideration is the graft-to-vein anastomosis of a vascular access graft. Suggested redesigns reduce several hemodynamic parameters (i.e., the WSSG, WSSAG, and normal pressure gradient [NPG]), thereby reducing the likelihood of restenosis, especially near the critical toe region.