This thesis presents the adaptation of the numerical procedure of modeling the extension – inflation experiment for arterial replicas fabricated by additive technology. Arterial replicas were designed based on histological analysis of the arterial wall clarified in Chapter 2, where the basic constituents and their influence on the overall mechanical behavior are described. Such a complex artery structure with highly nonlinear mechanical behavior was replicated by simultaneously printing two materials enabled by PolyJet 3D additive technology presented in Chapter 5. Ultimately, the mechanical behavior of such replicas was tested by the extension – inflation experiment because it perfectly mimics the in vivo multiaxial artery loading conditions, according to Chapter 3. The aim of this work was to take into account any significant factor that may affect the numerical results. This primarily implies the influence of the choice of material model and the associated material parameters of 3D printed materials. Since the theory of hyperelasticity is used, a brief overview of selected material models (neo-Hooke and Mooney-Rivlin) is presented in Chapter 6. However, as such models cannot be described by the theory of elasticity, the mechanical background of such materials was initially explained through continuum mechanics. In addition to the above mentioned factor, the influences of assigning an individual boundary condition and modeling the relationship between printed materials were examined, presented in more detail in Chapter 8. With a precisely defined numerical procedure, it would be possible to predict the mechanical behavior of other arterial replica geometries with different combinations of base materials. This would significantly reduce the number of required experiments and material consumption. Therefore, by evaluating the effects of changes of certain factors, the optimal numerical description of the experiment, indicated in Chapter 9 and 10, was chosen.