Stable crystal structures of wurtzite (w-BP) and recently discovered rhombohedral (rh-BP) polymorphic modifications of boron phosphide were obtained based on crystal chemistry rationale and unconstrained geometry optimization calculations within the density functional theory (DFT), and compared with known cubic polymorph (c-BP). Both w-BP and rh-BP are mechanically (elastic constants) and dynamically (phonons) stable and exhibit thermodynamic and mechanical properties very close to those of c-BP. The electronic band structures of all BP polymorphs depict semi-conducting behavior with band gap magnitudes close to 2 eV.