Structure, energetic characteristics, and the vibrational spectrum of reidite (ZrSiO₄ polymorph isostructural with sheelite) were studied by periodic density-functional calculations and compared with those of zircon. The computed structural parameters are in a good agreement with known data. The calculations provide a nonempirical estimation of the elastic constants of this material. Making use of the results of the computations a complete assignment of the phonons at the Γ point is proposed that accounts for features observed in the infrared and Raman spectra of reidite. The comparison of atomic displacements in the vibrational modes of the reidite and zircon structures permits to explain differences in their vibrational spectra in terms of structural peculiarities of the two lattices. Analysis of calculated effective charge tensors points to the validity of the two-body charge redistribution model and gives an estimation for the values of the corresponding charge transfer parameters.