Additive manufacturing methods, commonly known as 3D printing, allow more sophisticated designs to be created. Willingly designed substructures incorporated into the solid open up new possibilities for uncommon macroscopic deformation behavior. Such a man-made structure is also referred to as a metamaterial. A detailed simulation of a polymer-based metamaterial is challenging but accurately possible by means of the theory of elasticity. In this study, we present experimental investigations of a metamaterial composed of pantographic substructures of different internal geometry. The pantographic structures show an unexpected type of deformation, which can be modeled via elasticity with the aid of direct numerical simulation by using the Finite Element (FE) method. In other words, a detailed mesh is generated involving the substructure. The metamaterial is additively manufactured out of a common polymer showing nonlinear elastic deformation and, therefore, hyperelastic material models are used. Specifically, analytical solutions of a circular cylinder are examined and compared in the case of extension and torsion in order to comprehend the effects of the coefficients inherent to the energy function of the hyperelastic model. Finally, FE computations of pantographic structures are performed and compared with the experimental measurements.