In hypertension, aging and certain types of arterial disease, central elastic arteries become stiffer and hence the central pulse pressure is augmented due to the increase in pulse wave velocity (PWV) 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 (e.g. radial) pressure waveforms. A feasibility study for the non-invasive 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 propagative 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, the brachial artery pressure contours under the pneumatic cuff were simulated. Also, the combined model was able to illustrate how these pressures transmit through the arm to the cuff’s external wall and produce a strain contour. The effects of aortic stiffness, aortic geometrical variations, heart rate and cuff pressure were investigated by simulating the model at different parameters and observing the pressure and strain augmentation and the timing of the return of the reflected wave. This work was done as part of the development of a non-invasive diagnostic device by Pulsecor Ltd. The model results obtained in this work are in agreement with published experimental results and the strain contours obtained using the device and hence can be used to develop the device’s stiffness estimation algorithm.