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Functionally graded cellular materials, which combine cellular materials with a gradient of properties, have been recently investigated as cores of sandwich panels. The present work aims to evaluate the flexural properties of functionally graded cellular structures with a gradient of cell thickness on configurations recently proposed. The structures hexagonal honeycomb (Hr), lotus (Lt), and hexagonal honeycomb with Plateau borders (Pt) were designed with three different gradients of cell thickness. The parts were manufactured by material extrusion using FFF (Fused Filament Fabrication). To evaluate the mechanical properties, three-point bending tests were conducted, both experimentally and by numerical modelling, by means of the finite element method. The materials used were polylactic acid (PLA) and aluminum. Although experimental and numerical results exhibited some deviations, they revealed the same trends. The results showed that the stiffness and the absorbed energy of the graded Hr, Lt and Pt structures, made of PLA, are higher than such values for the regular hexagonal honeycombs. For the same gradient of cell thickness, the lotus structure tends to exhibit the highest stiffness and absorbed energy, while the hexagonal honeycomb arrangement achieves the largest value of strength. Graded aluminum specimens also attain higher values of stiffness, strength and absorbed energy in comparison with non-graded hexagonal honeycomb configurations. Thus, the use of gradients of cell thickness can promote structures with higher stiffness and absorbed energy, which may compete with the conventional structures of sandwich panel cores.