Abstract: The present study on the representative volume element (RVE) of honeycomb structures shows that, by compared with the homogeneous boundary conditions (HBCs), a more accurate result is obtained by using the periodic boundary conditions (PBCs). Based on the RVE with the PBCs, tensile tests of the self-similar hierarchical honeycombs (SSHHs) along the two in-plane directions were simulated. The effects of the porosity and the hierarchical length ratio were especially examined. The numerical results show that a large in-plane anisotropy in the SSHHs is observed. The SSHHs fails at the horizontal-links when it is subjected to a tension along the armchair direction. But when it is subjected to a tension along the zigzag direction, in case of the SSHHs with the edge of node-hexagon greater than the wall thickness and a long length of the hypotenuse-links, it will break down twice respectively at the node-hexagon and the hypotenuse-links, otherwise it breaks down once at the hypotenuse-links. It also can be seen that the tensile strength decreases with the increase of either the porosity or the hierarchical length ratio.