The compression Young's modulus and strength of lattice structures with porosity between 47.8% and 82.6% produced by Selective Laser Melting (SLM) of a Ti6Al4V powder were investigated. The Young's modulus and yield strength range from 1 GPa to 20 GPa and from 10 MPa to 250 MPa, respectively. On increasing porosity, both stiffness and strength decrease. When porosity increases above 60-65%, the strength shows an accentuated decrease compared to the stiffness decrease. The absence of struts parallel to the loading direction in the lattice structure allows to achieve higher yield strength than other structures having the same Young's modulus.