Titanium-based alloys are still fascinating materials of today's technology with prevalent use in aviation, biomaterial and automobile industries because of their superior mechanical properties. Further, Ti-5Al-XSn alloys can be defined as the second popular grades after the pioneer Ti-6Al-4V (Ti64) grades. Although it is possible to find many experimental and theoretical studies dealing with many diverse physical and mechanical features of Ti64 alloys, both experimental and theoretical surveys for Ti-5Al-XSn alloys are still lacking. To make up this shortage on Ti-5Al-XSn alloys, we performed this theoretical work for Ti-5Al-XSn (X = 2.5%, 3%, 3.5%, 4%, 4.5% and 5% wt.) alloys, within density functional theory (DFT) calculations and revealed the elastic, mechanical and anisotropic properties of the mentioned series of Ti-5Al-XSn alloys. Calculated elastic constants confirm the mechanical stability of alloys for all compositions. Moreover, increasing Sn element leads to the increment of ductility, machinability and elastic anisotropy of these alloys. In contrast, the hardness of the alloys shows a clear decrement by increasing the Sn content.