The crystal structure, phonon spectrum, and elastic constants of a series of rare-earth germanates (including yttrium germanate R2Ge2O7 (R = Tb–Lu, Y)) with a tetragonal structure have been ab initio calculated within the density functional theory. The frequencies and types of fundamental vibrations and the intensities of IR and Raman modes are determined. The degrees of participation of ions in each mode are determined by analyzing the displacement vectors obtained as a result of the ab initio calculations. The calculations have been performed for the first time; there are no corresponding experimental data for the entire series of compounds (except for the IR and Raman spectra of yttrium germanate). The performed calculations made it possible to interpret and supplement the known data in the literature on IR and Raman spectra of yttrium germanate Y2Ge2O7.