  The crystal structure, mechanical properties and electronic structure of
ground state BeH$_{2}$ are calculated employing the first-principles methods
based on the density functional theory. Our calculated structural parameters at
equilibrium volume are well consistent with experimental results. Elastic
constants, which well obey the mechanical stability criteria, are firstly
theoretically acquired. The bulk modulus \emph{B}, Shear modulus \emph{G},
Young's modulus \emph{E} and Poisson's ratio $\upsilon$ are deduced from the
elastic constants. The bonding nature in BeH$_{2}$ is fully interpreted by
combining characteristics in band structure, density of state, and charge
distribution. The ionicity in the Be$-$H bond is mainly featured by charge
transfer from Be 2\emph{s} to H 1\emph{s} atomic orbitals while its covalency
is dominated by the hybridization of H 1\emph{s} and Be 2\emph{p} states. The
valency in BeH$_{2}$ can be represented as Be$^{1.99+}$H$^{0.63-}$, which
suggests that significant charge transfer process exists.
