The elastic and structural properties of Aluminum-doped Gallium Arsenide at different pressure have been investigated by using the first-principles density functional theory. In order to calculate the exchange correlation potentials, the exchange and correlation potential is determined by the generalized gradient approximation parameterized by Perdew Burke Ernzerhof and local density approximation. The results showed the decrease of the lattice constants with increasing pressure and the bulk modulus increase from increasing pressure of binary Gallium Arsenide and their ternary alloy by both the approximations mentioned above. This results show a good agreement is found between the theoretical and the experimental available data. The elastic constants, Young modulus, Bulk modulus, Shear modulus, Poisson’s ratio and Debye temperatures of Gallium Arsenide binary and their ternary alloy as function of pressure have been calculated for the first time. The results provide a theoretical reference for doping of Gallium Arsenide with Aluminum atom at different pressures.