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The aim of our study is to investigate materials based on polylactic acid (PLA) composites and fibrin hydrogels. These materials will be used in the development of bioresorbable vascular grafts produced by additive manufacturing. Additive manufacturing technologies allow tubular objects to be designed in patient-specific 3D geometries, making them suitable for complex shapes such as the anatomy of the human aortic arch. A bioresorbable material composed of multiple polymers that mimics the structure and function of a living blood vessel should offer the advantage of a temporary scaffold that would dissolve after a period of arterial mechanobiological remodeling resulting in a neo-artery. This will be the final stage of our project. Before reaching this stage, we decided to start the study by investigating the mechanical properties of currently commercially available Gore-Tex vascular substitutes and compare their mechanical properties with PLA-PHB 3D printed materials. In our paper, we present the results of tensile tests carried out with blood vessel samples, Gore-Tex vascular substitutes, and 3D printed PLA-PHB composites. The materials were found to be nonlinear and anisotropic. They exhibited significant viscoelastic manifestations. This is especially true for Gore-Tex. All three types of materials differ significantly from each other mechanically. Regression analysis of the experiments identified nonlinear elastic constitutive models for the tested materials.