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Ab initio calculations are becoming increasingly useful to engineers interested in designing new alloys, because these calculations are able to accurately predict basic material properties only knowing the atomic composition of the material. In this paper, single crystal elastic constants of 11 bcc Mg–Li alloys are calculated using density functional theory (DFT) and compared with available experimental data. Based on DFT determined properties, engineering parameters such as the ratio of bulk modulus over shear modulus (B/G) and the ratio of Young’s modulus over mass density (Y/ ρ) are calculated. Analysis of B/G and Y/ρ shows that bcc Mg–Li alloys with 30–50 at.% Li offer the most potential as lightweight structural material. Compared with fcc Al–Li alloys, bcc Mg–Li alloys have a lower B/G ratio, but a comparable Y/ ρ ratio. An Ashby map containing Y/ ρ vs B/G shows that it is not possible to increase both Y/ ρ and B/G by changing only the composition of a binary alloy.