Quadratic configuration interaction calculation (QCISD) and B3LYP methods have been used to optimize the possible ground-state structures of H2, BeH and BeH2 molecules. The results show that their ground electronic states are H2(1Σg), BeH(2Σ) and BeH2(1Σg); the stable structure of BeH2molecule is of D∞h symmetry. The Murrell-Sorbie potential energy function with 8 parameters of BeH and H2 molecule has been derived from the least square method, according to which spectral data and force constants are deduced. The analytical potential energy function of BeH2 is derived from the many-body expansion theory. Since BeH2(D∞h) formed from H+BeH has a deep potential trap, the complex com pound molecule of H-Be-H is easily formed. The reaction of Be+H2→HBeH　with ΔH=-1.4654eV is an exothermic reaction.