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A first-principles plane wave method with the ultrasoft pseudopotential scheme in the frame of the density functional theory (DFT) is performed to calculate the lattice parameters a and c, the bulk modulus B0 and its pressure derivative B of the zinc-blende GaAs (ZB-GaAs), rocksalt GaAs (RS-GaAs), CsCl-GaAs, NiAs-GaAs and wurtzite GaAs (WZ-GaAs). Our results are consistent with the available experimental data and other theoretical results. We also calculate the phase transition pressures among these different phases. The results are satisfactory.