In this work, Acrylonitrile-Butadiene-Styrene model structures were manufactured by FDM, and their mechanical behaviour investigated under compression, both at small and at large strains. The structure design strategy adopted, based on the use of circular cross-section beam-like elements formed under controlled conditions, led to obtain open-cell structures (with a porosity degree of ≈ 65%) composed of unit cells with different shapes and dimensions assembled to form regularly repeating patterns. The stress-strain behaviour, from cube- and prism-shaped specimens with different sizes and loaded along different directions, was discussed in the light of the outcomes from (i) cyclic compression experiments and (ii) morphological analyses of cryogenic fracture surfaces of specimens compressed at high strain levels. The response along the 3D-stacking direction was traced back to the elastic-plastic case, with non-recoverable strain starting to accumulate between 3% and 5% strain and structure densification starting below 20%. The specimen size effects turned out to be little pronounced. Slightly higher levels of stiffness and strength were measured for the largest cube. This result was discussed on the basis of the peculiar morphology of the structure examined.