Lattice structures are used in engineering industries because of their good mechanical properties, including high stiffness, high strength, as well as specific energy absorption and fracture toughness. They are often built with hierarchical structuring, which adds complexity to them, while improving their mechanical properties. Unfortunately, there is limited literature available regarding how hierarchical structuring affects the stress levels, stress concentration, and deflection of hierarchicallattice structures. In this work, Ti6Al4V (ELI-Extra low interstitial) hierarchical honeycomb (HC) models of order one at the vertices comprising hexagonal, circular, and triangular polygons, were analysed numerically. The effects of hierarchical configuration on stress levels, stress concentration, and deflection of the hierarchical HC models were compared to those of the regular HC model, for the case of out-of-plane loads in uniaxial compression tests. In terms of load-bearing capacity and stiffness for loads applied in the in-plane x-direction, the hierarchical HC model with hexagonal substructures at the vertices ranked higher than the models with circular or triangular substructures. For loading in the in-plane y-direction, the hierarchical HC model with circular substructures at the vertices ranked highest. The highest load-bearing capacity and stiffness for loading in the in-plane and out-of-plane directions was observed for in-plane loading in the x-direction. Deflections were smaller for loading in the two in-plane directions than in the out-of-plane direction. In-plane loading at the vertices of these structure gave rise to high stress concentrations at the points of loading. Loading the numerical models in the plane, directly at the apex regions led to the highest magnitudes of stress and deflection. Hierarchical honeycomb structures with lower sharp changes of geometry at the vertices minimized the concentration of stresses there.