Cellular structures subjected to compressive loads provide a reliable solution for improving safety. As a member of cellular material, auxetic metamaterials can enhance performance according to the definition of the negative Poisson ratio. In conjunction with Rapid Prototyping by Additive Manufacturing methods, complex structures can be manufactured using a wide range of materials. This paper debuts the development process of a reliable material model that is useful for the numerical simulation, and further details and investigates the performance indicators of an auxetic structure, namely anti-tetra-chiral. These indicators are related to the force developed during the plateau stage, the length of the plateau stage, and the nominal dimensions of the structure to avoid buckling during compression. Two new indicators discussed in this paper aim to provide a complete set of performance indicators. The first analytical solution provides the displacement of the circular nodes during the compression. The second analytical solution estimates the strain developed in the ligaments. Considering the performance of the processed material, this analysis aims to determine whether the structure can develop the complete plateau stage or whether premature failure will occur.