Crystal structure and phonon spectra R2TiO5 (R = Nd, Sm) were studied within the framework of density functional theory and MO LKAO approach. The calculations were performed by using hybrid functional that takes into account both local and nonlocal (at the Hartree-Fock formalism) exchange. The coordinates of the ions in the unit cell and the lattice constants are calculated. The fundamental vibration frequencies of R2TiO5 (R = Nd, Sm) were calculated. The relative intensities of the Raman lines and the intensity of the IR-active modes have been calculated. The elastic constants of the crystal have been calculated at the first time.