The degeneration of the vascular wall tissue induces a change of the arterial stiffness, i.e., the capability of the vessel to distend under the pulsatile hemodynamic load. In the literature, the aortic stiffness is usually computed following a simple deterministic approach, in which only the maximum and the minimum values of arterial diameter and blood pressure over the cardiac cycle are considered. In this paper, we propose a stochastic approach to assess the stiffness, and its spatial variation, of a given aortic region exploiting patient-specific geometrical data derived from computed tomography angiography (CTA). In particular, the arterial stiffness is computed linking the aortic kinematic information derived from CTA with pressure waveforms, generated using a lumped parameter model of the arterial circulation. The proposed method is able to include the uncertainty of the input variables as well as to use the entire diameter and blood pressure waveforms over the cardiac cycle rather than only their maximum and minimum values. Although the efficiency and accuracy of the proposed method are tested on a single patient-specific case, the proposed approach is powerful and already possesses the ability to evaluate regional changes of stiffness in human aorta using noninvasive data. The final objective of our paper is to support the adoption of techniques such as CTA as a standard tool for diagnosis and treatment planning of aortic diseases.