The composite wave variational version of the APW method has been used in conjunction with the LCAO interpolation scheme to compute the energy bands and the joint density of states of the compounds BeS, BeSe and BeTe at various symmetry points and axes of the Brillouin zone. From these computed bands, all three materials are found to be semiconductors having band gaps of 6.10 eV, 4.75 eV and 1.49 eV, respectively. From the joint density of state characteristics, various optical transitions have also been predicted. The results have been favourably compared with those of Stukel. Since BeTe is found to be a small-gap semiconductor, its possible technological importance has also been emphasized.