The identification of the proper parameters of material models plays a crucial role in the design of production technologies, especially in the case of modern materials with diversified properties under different boundary conditions. The procedure of identification is usually based on an optimization algorithm that uses sophisticated numerical simulations as a part of the goal function and compares the obtained results with experimental tests. Despite its reliability, such an approach is numerically inefficient. This paper presents the concept of how to replace the most numerically-demanding part of the identification procedure with metamodels, allowing us to maintain uniform result quality. The computer system, which allows us to manage input data, metamodels, and calculations, is proposed and described in detail in this paper. Finally, the proposed approach is validated on the basis of tests performed in the laboratory.