The scope of this PhD is 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. These parameters need to be estimated from experiments (in the case when tissue is available) or from non-invasive, in vivo measurements. In vivo parameter estimation is, of course, more clinically relevant. Ideally, the loadings and displacement are measured in two directions and, based on this experimental data points, parameters for the mathematical description are estimated. In vivo, it’s is currently impossible to obtain the loadings in two directions and the loading range is limited to physiological pressures. The developed method is introducing additional assumptions to tackle this limitations. The method developed in this thesis is used on both animal and human data sets with a goal to compare in vivo parameters with the parameters obtained in vitro (by preforming planar biaxial tests).