The nature of the lattice instability connected to the structural transition and superconductivity of (Sr,Ca)3 Ir 4 Sn 13 is not yet fully understood. In this work density functional theory (DFT) calculations of the phonon instabilities as a function of chemical and hydrostatic pressure show that the primary lattice instabilities in Sr 3 Ir 4 Sn13 lie at phonon modes of wave vectors q=(0.5,0,0) and q=(0.5,0.5,0). Following these modes by calculating the energy of supercells incorporating the mode distortion results in an energy advantage of -14.1 and -9.0 meV per formula unit, respectively. However, the application of chemical pressure to form Ca3 Ir 4 Sn 13 reduces the energetic advantage of these instabilities, which is completely removed by the application of a hydrostatic pressure of 35 kbar to Ca3 Ir 4 Sn 13. The evolution of these lattice instabilities is consistent with the experimental phase diagram. The structural distortion associated with the mode at q=(0.5,0.5,0) produces a distorted cell with the same space-group symmetry as the experimentally refined low-temperature structure. Furthermore, calculation of the deformation potential due to these modes quantitatively demonstrates a strong electron-phonon coupling. Therefore, these modes are likely to be implicated in the structural transition and superconductivity of this system.