The Beetle Elytron Plate (BEP) is a new type of biomimetic sandwich core developed as a potential replacement of classical honeycomb cores in sandwich panels. This work investigates the out-of-plane engineering elastic constants, including Young's and pure shear moduli of parametric BEP cellular topologies. The BEP core configurations are simulated using Finite Element models, with both full-scale and representative unit cells for asymptotic homogenization. The numerical models are also validated by flatwise compression and out-of-plane pure shear loading experiments performed according to ASTM standards. The benchmarked models are then used to perform a parametric analysis of the beetle elytra cellular cores against their geometry characteristics. Results show that the out-of-plane Young's modulus E3/Esand the transverse pure shear modulus G31/Es of both BEP configurations are larger than those of the classic hexagonal honeycombs and increase when the size of the unit cell cylinders, or rib thickness become large. The specific shear moduli of the beetle-elytra inspired honeycombs are however lower than those of classical pure hexagonal honeycomb configurations, although the added presence of cylinders within the cell configuration offers opportunities for tailoring the design of multifunctional cores.