The influence of pressure on the structural and elastic properties of ScM (M = Rh, Cu, Ag, Hg) compounds has been performed by using ab initio approach pseudopotential plane-wave method based on the density functional theory within the generalized gradient approximation (GGA). The optical properties have been investigated under zero pressure. It is found that the optimized lattice parameters for all metals are in good agreement with the experimental data and other available theoretical values. We obtained three independent elastic constants C ij (C 11, C 12 and C 44 ) and various elastic parameters such as bulk modulus B, shear modulus G, Young's modulus E, B/G, Poisson's ratio ν and anisotropy factor A as a function of pressure. In addition, the mechanical stability and ductile/brittle nature are also investigated from the calculated elastic constants. The study of optical properties reveals that all of these compounds possess good absorption coefficient in the high energy region and the refractive index of all these compounds is higher in the low energy region and gradually decreased in the high energy region. All these calculations have been carried out using the CASTEP computer code.