The goal of this PhD was to develop a method for noninvasive estimation of arterial material properties. The arterial tissue is nonlinear, anisotropic and heterogeneous, and as such needs to be described with complex mathematical equations that contain multiple parameters. If the tissue is available, these parameters can be estimated from ex situ mechanical experiments. In vivo, they need to be obtained from currently available noninvasive or minimally invasive measurements. However, the fact that the amount and quality of possible in vivo measurements is limited, and that vascular tissue is anisotropic and subjected to large nonlinear deformations, makes the estimation of material properties very challenging. The mentioned challenges were tackled within the scope of this PhD. The performance of the properties obtained with the newly developed method were evaluated with a standard ex situ experimental estimation approach. Finally, the potential of applying the method in a real clinical scenario was investigated by applying the method to clinical data. This was done with two real data sets. The first data set was obtained on healthy human common carotid arteries. The second data set came from human ascending thoracic aortic aneurysmal tissue.