In the present study, two irregular honeycombs are manufactured by a 3D printer and tested under compression. Experimental observation shows that the first fracture of cell walls is significantly critical, which is indeed the onset of global failure of honeycombs. To predict the onset of global failure of honeycombs, failure criteria based on stress or strain at integration point level need to be used, which is difficult to realize due to stress singularity at cell wall joints. To circumvent this issue, a mesh level, 40 elements within each cell wall, is chosen in FE analysis so that numerical results at cell wall joints are close to engineering solutions. Failure criteria based on von Mises stress, equivalent plastic strain, tensile plastic strain, surface tensile stress and bending moment are then employed to predict the first fracture of cell walls. It is found that failure criteria based on von Mises stress, equivalent plastic strain, tensile plastic strain yield the same predictions which are within 9% of experiment value for strength and within 24% for strain at failure. The cell walls which are predicted to be the most likely to fracture first in the honeycombs agree well with these cell walls that rupture first in experiments.