In hypertension and aging, central elastic arteries become stiffer and hence the central pulse pressure is augmented due to the increase in the pulse wave velocity and the early return of reflected waves to the heart from the periphery. Valuable information on arterial properties, such as stiffness, can be obtained from both central (aortic) and peripheral (radial) pressure wave forms. A feasibility study for the noninvasive estimation of arterial stiffness using pressure waves detected by a pneumatic cuff wrapped around the upper arm is presented. The propagation and reflection of arterial pressure waves (generated by the heart) in the central elastic arteries are simulated using a simplified water hammer acoustic model. Furthermore, a lumped parameter model is used to describe the transmission of the pressure waves from the brachial artery to the cuff external wall. By combining the two models, we were able to simulate the pressure contours in the brachial artery and illustrate how these pressures transmit to the cuff’s external wall. The effects of aortic stiffness are investigated by simulating the model at different values of aortic elastic moduli and observing the pressure augmentation and the timing of feature points. This work was done as part of the development of a noninvasive diagnostic device by Pulsecor Ltd. The model results obtained in this work are in agreement with published experimental results and the device output; hence, the model can be used to develop the device’s stiffness estimation algorithm.