Using first principles calculations, we have studied the structural and elastic properties of SrTMO 3 (TM = Rh, Ti, Mo, Zr) under pressure by the plane wave pseudopotential method based on the density functional theory (DFT) within the generalized gradient approximation (GGA). The optical properties have been investigated under zero pressure. It is observed that the calculated lattice parameters are in good agreement with the available experimental result and previous theoretical results. From the static finite strain method, the independent elastic constants and their pressure dependence are calculated. The effect of pressures, up to 60 GPa, on the lattice parameters, bulk modulus B, Shear modulus G, B/G, Poisson's ratio ν, anisotropy factor A are also investigated. This is the first theoretical prediction of the elastic and optical properties of SrTMO 3 compounds under pressure. All these calculations have been carried out using the CASTEP computer code.