The pressure dependence of the electronic, elastic, vibration and optical properties for ScXSb (X = Ni, Pd, Pt) half-Heusler compounds in cubic MgAgAs-type structure was systematically performed using the density functional theory with PAW method. The computed lattice parameters are in reasonable accord with available experimental data. Using the elastic constants and related parameters, the crystal rigidity and mechanical stability were discussed. The calculated electronic band structures revealed that ScNiSb and ScPdSb have an indirect gap in Gamma-X Brillouin zone, whereas ScPtSb has a direct band gap in Gamma-Gamma Brillouin zone. We also presented phonon dispersion relation and density of phonon states. It is found that the considered structure is stable for three compounds between 0 and 50 GPa pressure. The optical properties were also predicted at various pressures.