Purpose: This paper aims to describe the obtainment of Ti-6Al-4V parts with a hierarchical arrangement of pores by additive manufacturing, aiming at designing orthopedic implants. Design/methodology/approach: The experimental methodology compares microstructural and mechanical properties of Menger pre-fractal sponges of Ti-6Al-4V alloy, manufactured by laser powder bed fusion (LPBF) and electron beam powder bed fusion (EBPBF), with three different porosity volumes. The pore arrangement followed the formation sequence of the Menger sponge, with hierarchical order from 1 to 3. Findings: The LPBF parts presented a martensitic microstructure, while the EBPBF parts presented an α + ß microstructure, independently of its wall thickness. The LPBF parts presented higher mechanical resistance and effective stiffness than the EBPBF parts with similar porosity volume. The stiffness values of the Menger pre-fractal sponges of Ti-6Al-4V alloy, between 4 and 29 GPa, are comparable to those of the cortical bone. Furthermore, the deformation behavior presented by the Menger pre-fractal sponges of Ti-6Al-4V alloy did not follow the Gibson and Ashby model's prediction. Originality/value: To the best of the authors' knowledge, this is the first study to obtain Menger pre-fractal sponges of Ti-6Al-4V alloy by LPBF and EBPBF. The deformation behavior of the obtained porous parts was contrasted with the Gibson and Ashby model's prediction.