Additively manufactured cellular materials enable customized structural implants with superior osseointegration potential and mechanical properties better matched to bone. In this investigation, the compression response of Ti–6Al–4V alloy cellular materials comprising a simple cubic array of 2.00 mm diameter spherical voids with a 1.90 mm inter‐void spacing are studied. Finite element analysis (FEA) shows that the lattice exhibited cubic symmetry with values for Young's modulus (E), Poisson's ratio, and shear modulus in the range of 28.5–29.5 GPa, 0.18–0.20, and 5.4–6.0 GPa, respectively. Compression tests carried out on cylinders with the same cellular structure fabricated by selective laser melting also show a strong dependence of elastic and plastic properties on orientation. Compression normal to the {100} plane of the simple cubic cell gives the highest E and strength, while compression normal to the {110} and {111} planes give lower values. The experimental E values for the {100} and {111} orientations show good agreement with the FEA results, but the {110} orientation shows lower values of E compared to the FEA predictions. Ultimate compressive failure of the cylinders occurred by gross slip along the {100} planes of the void array – coinciding with the slip planes for the simple cubic system.