The angle of arterial tapering increases with ageing, and the geometrical changes of the aorta may cause an increase in central arterial pressure and stiffness. The impact of tapering has been primarily studied using frequency‐domain transmission line theories. In this work, we revisit the problem of tapering and investigate its effect on blood pressure and pulse wave velocity (PWV) using a time‐domain analysis with a 1D computational model. First, tapering is modelled as a stepwise reduction in diameter and compared with results from a continuously tapered segment. Next, we studied wave reflections in a combination of stepwise diameter reduction of straight vessels and bifurcations, then repeated the experiments with decreasing the length to physiological values. As the model's segments became shorter in length, wave reflections and re‐reflections resulted in waves overlapping in time. We extended our work by examining the effect of increasing the tapering angle on blood pressure and wave intensity in physiological models: a model of the thoracic aorta and a model of upper thoracic and descending aorta connected to the iliac bifurcation. Vessels tapering inherently changed the ratio between the inlet and outlet cross‐sectional areas, increasing the vessel resistance and reducing the compliance compared with non‐tapered vessels. These variables influence peak and pulse pressure. In addition, it is well established that pulse wave velocity increases in an ageing arterial tree. This work provides confirmation that tapering induces reflections and offers an additional explanation to the observation of increased peak pressure and decreased diastolic pressure distally in the arterial tree.