This paper deals with the determination of the equivalent elastic and strength properties of triply periodic minimal surfaces (TMPS) lattice structures. Specifically, primitive and gyroid TPMS are analyzed, and their macroscopic properties, in terms of stiffness and strength, are derived as a function of the relative density. These properties are derived through numerical homogenization on the representative volume element (RVE) and via numerical analyses on specimens composed of an array of RVEs and compared to data available in the literature. These findings may potentially aid the creation of functionally graded cellular materials with variable density, optimizing structural stiffness and mass.