In energy absorption applications, post-yield behaviour is important. Lattice structures, having low relative densities, are an attractive way to obtain effective material properties that differ greatly from that of the parent material. These properties can be controlled through the manipulation of the cellular geometry, a concept that has been made significantly more attainable through the use of additive manufacturing (AM). Lattice structures of various geometries were designed, additively manufactured and tested to assess their structural integrity as well as to investigate the effect of varying the cell geometry on the overall performance of the structures. Uniaxial tensile and compressive tests were carried out on bulk material AM samples made of 316L, followed by tests on the lattice structures. Finite element (FE) analysis was also carried out and the results compared to the experimental data. The FE simulations were able to accurately predict the elastic response of both structures; however, the post-yield behaviour did not closely match the experimental data due to inadequate beam contact resolution in the FE model. The FE model yield stress was also overestimated in the regular lattice due to the presence of manufacturing defects found only in the manufactured test samples. The stochastic structure, both experimentally and in the FE model, displayed a transition in the elastic stiffness from a lower to a higher stiffness in the elastic region. This is due to changing load paths within the lattice from the beams in contact with the compression platens to the rest of the structure. This phenomenon did not occur within the regular structure.