The low-lying electronic states of Be2H2 have been investigated using an ab initio methodology in order to explore the nature of the Be-Be bonding in this tetra-atomic molecule. The donation of two electrons from the antibonding molecular orbital mainly associated with Be-2 to orbitals mainly associated with the Is of the H atoms is found to be responsible for the strong Be-Be bond in this tetra-atomic molecule compared with the Be-2 diatomic. In addition to the linear form, a cyclic isomer of Be2H2 has been identified at about 1.47 eV above the linear structure. This structure results from an avoided crossing taking place above the lowest dissociation limit giving two BeH fragments. For the linear structure, a six dimensional potential energy surface has been generated and the rovibrational levels have been computed variationally. The fundamental modes obtained are found to be in well agreement with those detected experimentally. For Be2H2 (Be2D2), the antisymmetric stretching mode nu(3) is computed at 2028.6 (1519.3) cm(-1).