Cellular solid materials are progressively becoming more predominant in lightweight structural applications as more technologies realize these materials can be improved in terms of performance, quality control, repeatability and production costs, when allied with fast developing manufacturing technologies such as Additive Manufacturing. In parallel, the rapid advances in computational power and the use of new numerical methods, such as Meshless Methods, in addition to the Finite Element Method (FEM) are highly beneficial and allow for more accurate studies of a wide range of topologies associated with the architecture of cellular solid materials. Since these materials are commonly used as the cores of sandwich panels, in this work, two different topologies were designed — conventional honeycombs and re-entrant honeycombs — for 7 different values of relative density, and tested on the linear-elastic domain, in both in-plane directions, using the Natural Neighbor Radial Point Interpolation Method (NNRPIM), a newly developed meshless method, and the Finite Element Method (FEM) for comparison purposes.