We use the boundary element method to study numerically the contact behaviors of an auxetic layer-substrate structure indented by a rigid indenter. The indenter considered in this paper is selected as a parabolic indenter. The layer-substate comprises the PLA for the layer and the bone-inspired cellular structure (BCS) for the substrate. In developing the boundary element method, the special fundamental solution for elastic bimaterials is used. Thus, no meshes are required on the contact surface between the layer and substrate, which is beneficial in computational and modeling the problem. With the boundary element method, numerical examples are provided, and we have shown that the computed solutions agree with the available solutions in the literature. Parametric studies have also been performed to study the influence of the BCS substrate and the layer on the indentation resistance of the structure. It was found that the BCS auxetic substrate and layer’s thickness significantly influenced the structure’s indentation stress and the indentation resistance of the structures.