The ab initio study of the structure and dynamics of the lattice, as well as the elastic properties of a row of rare-earth stannates R2Sn2O7 (R = La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu) has been carried out for first time. The IR and Raman spectra were calculated, the types of phonon modes were determined. The degree of participation of ions in phonon modes is determined. Modes with the absolute or predominant participation of oxygen in the 48f position, characterized by a shift x, were determined from an analysis of the displacement vectors obtained from the ab initio calculations. The elastic constants and the hardness HV have been calculated. The effect of hydrostatic compression on the crystal structure is investigated. It is shown that the degree of distortion of the octahedron containing the rare-earth ion changes little with pressure (up to 12 GPa). It is shown that the dependence of the unit cell volume on pressure is described by the Birch-Murnaghan equation of state of the third order.