There is a significant and unexplained drop in the band-gap pressure coefficients of III-V ternary semiconductor alloys grown as strained layers compared with the bulk binary values. For example, the drop for In x Ga 1รx As is about รฐ50xร meV/GPa. In the past, first order effects of pressure have been treated using linear elasticity and this fails to predict the observed pressure coefficients. Ideally strained layers would be treated using an equation of state valid for an arbitrary state of strain, however, such theory is not currently available. Here, we present work towards such an equation and an approximate analysis using non-linear elasticity theory that does account for the data observed. The analysis relies on treating the non-linear variation of the substrate and layer lattice constants and the variation of the Poisson's ratio with respect to pressure. The analysis is tested against experimental data for h001i-grown layers available in the literature. In addition, we present new results on layers grown in the h111i direction. This acts as a further test on the theory because it involves a different Poisson's ratio. The experimental results agree well with the predictions of the non-linear theory.