Sandwich panels have been widely used in many engineering applications where saving weight whilst maintaining high strength and stiffness is crucial. The increase in use of these structures highlights the need for a detailed study and development of new structural typologies to upgrade mechanical properties such as stiffness, strength and energy absorption. The sandwich panel cores are man-made cellular materials. The most common core is the two dimensional regular hexagonal cell shape, labelled honeycomb which has been used as the baseline of this study. Two new bioinspired natural structures were developed to find improvements in the performance of sandwich panel cores, particularly in the in-plane properties. Among all the large amount of structures that nature provides, enamel and bamboo were chosen. The compressive and flexural properties of these two innovative cellular structures were assessed and compared against the classic honeycomb. To carry out this comparison, all the arrangements were numerically simulated with the Abaqus software for different relative densities. Finally, the fused deposition modelling (FDM) technique was used to print some selected samples in polylactic acid (PLA) that were experimentally tested. The ultimate goal of this methodology was to validate the results from the finite elements simulations with experimental data. Results show that the mechanical properties depend on the core geometry and have a strong reliance on the relative density. Finally, for the same relative density, the bioinspired natural structures compete with the traditional core structures in what concerns to strength and stiffness.