Structural parameters, band-gap energies, and mixing enthalpies of Sc1-x In (x) As alloys were calculated using the full-potential linearized-augmented plane wave method. These calculations are based on density functional theory, within local density approximation, and generalized gradient approximation for the exchange and correlation potential. Given that the binary precursor compounds ScAs and InAs crystallize in rock-salt and zinc-blende, respectively, we made calculations for the ternary alloys in these two phases. The effect of composition x on structural parameters, band-gap energies, and mixing enthalpies was analyzed for x = 0, 0.25, 0.5, 0.75, 1. The effect of atomic composition on lattice constant, bulk modulus, and band-gap energy shows nonlinear dependence on concentration x. Deviations of the lattice constant from Vegard's law and deviations of the bulk modulus and gap-energy from linear concentration dependence were found. We have found a metallic character for rock-salt Sc1-x In (x) As alloys, while the zinc-blende Sc1-x In (x) As alloys are semiconductors. Our results show that the band-gap undergoes a direct ()-to-direct () transition at a given indium composition. The physical origin of the band-gap bowing in zinc-blende Sc1-x In (x) As alloys was investigated. To study the thermodynamic stability of Sc1-x In (x) As alloys, a regular-solution model was used. This resulted in lower mixing enthalpies for zinc-blende Sc1-x In (x) As alloys.