Abstract: Density functional theory is used to study the effect of asymmetric in-plane strain on various BiInO₃ phases. Structural relaxation is carried out to simulate the growth of coherently strained epitaxial films on (001) oriented orthorhombic perovskite substrates. The results are in particular analyzed with respect to commercially available substrates in order to assess the stabilization of new and fundamentally interesting BiInO₃ phases. We find that a pyroxene-like Pcca phase is energetically more favorable than the bulk-like Pna2₁ structure on standard cubic substrate materials, such as SrTiO₃. However, the presence of imaginary phonon modes suggests that this phase is dynamically instable. The bulk-like structure instead is stable over a wide range of lattice in-plane strain, but coherent growth requires substrates with unusually large lattice parameters. We suggest the use of lanthanate substrates in order to produce high-quality thin films of the bulk phase. Graphical abstract: [Figure not available: see fulltext.]