In this paper we present the results obtained from first-principles calculations of the effect of hydrostatic pressure on the strucural, elastic and electronic properties of (B3) boron phosphide, using the pseudopotential plane-wave method (PP-PW) based on density functional theory within the Teter and Pade exchange-correlation functional form of the local density approximation (LDA). The lattice parameter, molecular and crystal densities, near-neighbour distances, independent elastic constant, bulk modulus, shear modulus, anisotropy factor and energy bandgaps of (B3) BP under high pressure are presented. The results showed a phase transition pressure from the zinc blende to rock-salt phase at around 1.56 Mbar, which is in good agreement with the theoretical data reported in the literature.