Background The aim of the analysis is to develop design principles for a new material having properties similar to those of the natural aortic artery. This involves replacing the complex structure of the aortic wall with a new material with a layer-composite structure having the same strength and hemodynamic properties. The structure of the material used to construct the new aortic prosthesis consists of three layers. Inner layer contains important fibers arranged in two orthogonal directions: circumferential and axial. The fibers are embedded in a liquid matrix, which, due to the characteristics and properties of liquids, does not degrade or change its properties in contact with the moving fiber. The finite element method was used to develop the strength properties of the new material. Constitutive equations were defined to relate the state of stress and the state of strain in the material during its work. In the circumferential direction, the Young’s modulus was 790 kPa, and the fiber shape factor was 0.056. In the axial direction, the Young’s modulus was 440 kPa, the fiber shape factor was 0.067. The paper presents the process of optimizing the material model of a new bioprosthesis, which mechanically imitates the natural material of the aorta. A simple fiber structure was immersed in a liquid matrix and described using basic material parameters. This approach allows to obtain a material with non-linear characteristics and high compliance, not seen in previous prostheses made of Dacron.