Multilayer panels that have paper cores with hexagonal cells continue to have a limited application in furniture production. In contrast, there are no sandwich honeycomb panels with cores containing rectangular cells employed in this industry. Such cores should distinguish themselves by strong orthotropic advantages, in particular, for designing shelves and partitions of cabinet furniture. Hence, the objective of this study was to determine the effect of core rectangular paper cells on the mechanical properties of three-layer furniture panels. The authors decided to ascertain relative density and elasticity constants of the designed cells. The results of empirical experiments of cell elasticity moduli were compared with the results of the analytical calculations. The impact of sample width on their mechanical properties was determined. It was demonstrated that cores with hexagonal cells in furniture panels could be replaced by cores with rectangular cells.