In the framework of a unified ab initio approach, the phonon spectrum of yttrium stannate Y2Sn2O7 was calculated, the frequencies and types of IR and Raman modes were determined. From an analysis of the displacement vectors obtained in ab initio calculations, the degree of participation of ions in phonon modes is determined. The elastic constants and hardness of Y2Sn2O7 are calculated. The distance "impurity ion-ligand" in impurity centers Y2Sn2O7: Yb3 +, Y2Sn2O7: Eu3 +, Lu2Sn2O7: Yb3 +, Nd2Sn2O7: Gd3 +, Nd2Sn2O7: Tb3 + is calculated.