Arterial stiffness (AS), as assessed via pulse wave velocity (PWV), is a major biomarker for cardiovascular risk assessment in patients with chronic kidney disease (CKD). However, the mechanisms responsible for the changes in PWV in the presence of kidney disease are not yet fully elucidated. In the present study, we aimed to investigate the direct effects attributable to biomechanical changes in the arterial tree caused by staged renal removal, independent of any biochemical or compensatory effects. Particularly, we simulated arterial pressure and flow using a previously validated one-dimensional (1-D) model of the cardiovascular system with different kidney configurations: two kidneys (2KDN), one single kidney (1KDN), no kidneys (0KDN), and a transplanted kidney (TX) attached to the external iliac artery. We evaluated the respective variations in blood pressure (BP), as well as AS of large-, medium-, and small-sized arteries via carotid-femoral PWV (cfPWV), carotid-radial PWV (crPWV), and radial-digital PWV (rdPWV), respectively. Our results showed that BP was increased in 1KDN and 0KDN, and that systolic BP values were restored in the TX configuration. Furthermore, a rise was reported in all PWVs for all tested configurations. The relative difference in stiffness from 2KDN to 0KDN was higher in the case of crPWV (15%) in comparison with the increase observed for cfPWV (11%). In TX, we observed a restoration of the PWVs to values close to 1KDN. Globally, it was demonstrated that alterations of the outflow boundaries to the renal arteries with staged kidney removal led to changes in BP and central and peripheral PWV in line with previously reported clinical data. Our findings suggest that the PWV variations observed in clinical practice with different stages of kidney disease may be partially attributed to biomechanical alterations of the arterial tree and their effect on BP.