Based on density functional theory calculations, systematic calculations of the structural properties, elastic anisotropy and mechanical properties of boron alloying aluminum phosphide (BxAl1-xP) ternary mixed crystal have been presented. The results of the lattice parameters, band gaps, elastic constants and elastic modulus accord with the experimental and others published data well. The band structure which is described by CASTEP method indicates they are direct gap semiconductors for the composition x = 0.25, 0.50 and 0.75. Beyond that, we studied the Debye temperatures together with the acoustic velocities for all the BxAl1-xP alloys using the obtained elastic modulus. Finally, we depicted the three dimensional surface constructions to explain the elastic anisotropy using several calculated different anisotropic indexes in our work.