  Structural and elastic properties of Ba$_{2}$P$_{7}$X (X=Cl, Br, I) (Barium
Phosphide Halides) Zintl compounds have been investigated using the
pseudo-potential plane-wave (PP-PW) method based on the density functional
theory (DFT) within the generalized gradient approximation (GGA-PBESOL). The
calculated lattice constants and internal parameters are in a good agreement
with the experimental results reported in literature. In this paper, we present
an investigation of the relative changes of the structural parameters and
elastic constants as function of hydrostatic pressure. Isotropic elastic moduli
and their related properties for single-crystal and polycrystalline phase,
including the namely bulk modulus, shear modulus, Young's modulus, Poisson's
ratio, elastic anisotropy indexes, Pugh's indicator of brittle/ductile
behavior, elastic wave velocities and Debye temperature have been estimated
from $C_{ij}$ using Voigt, Russ and Hill approximations. Two different methods
have been used to study the elastic anisotropy of these compounds.
