The mechanical properties, such as the elastic constants C-11, C-12, C-44, and bulk, Young's, and shear moduli, of a GaxIn1-xAsyP1-y alloy lattice matching to a GaAs substrate are calculated for various As concentrations. The calculations are based on the pseudo-potential method within the virtual crystal approximation containing the effective disorder potential. The variations of the studied properties with pressure and temperature are investigated. A comparison between the calculated results and the available published data for binary parent compounds shows that they have good agreement, while the calculated results for the quaternary alloys at various temperature and pressure may be taken as a reference.