SnS has potential technical applications, but many of its properties are still not well studied. In this work, the structural, thermodynamic, elastic, and electronic properties of α-SnS have been investigated by the plane wave pseudo-potential density functional theory with the framework of generalised gradient approximation. The calculated pressure-dependent lattice parameters agree well with the available experimental data. Our thermodynamic properties of α-SnS, including heat capacity C P , entropy S , and Gibbs free energy relation of –( G T – H 0 ) curves, show similar growth trends as the experimental data. At T =298.15 K, our C P =52.31 J/mol·K, S =78.93 J/mol·K, and –( G T – H 0 )=12.03 J/mol all agree very well with experimental data C P =48.77 J/mol·K and 49.25 J/mol·K, S =76.78 J/mol·K, and –( G T – H 0 )=12.38 J/mol. The elastic constants, together with other elastic properties, are also computed. The anisotropy analyses indicate obvious elastic anisotropy for α-SnS along different symmetry planes and axes. Moreover, calculations demonstrate that α-SnS is an indirect gap semiconductor, and it transforms to semimetal with pressure increasing up to 10.2 GPa. Combined with the density of states, the characters of the band structure have been analysed in detail.