A lattice-dynamical formalism using the rigid-ion model due to Born and Huang is applied to the ferroelectric crystals ${\mathrm{PbTiO}}_{3}$ and ${\mathrm{BaTiO}}_{3}$, in the tetragonal phase. The model includes short-range interactions of axially symmetric type between various ions in the primitive cell and long-range Coulomb interactions. The stability conditions are worked out in the manner described by Katiyar and are used to determine several first-order derivative potential constants for the crystals. The number of potential constants was further reduced by considering the variation of radial force constants with the ion-ion distance, as given by the exponential formalism of Born and Mayer. Zone-center phonons and a few of the low-frequency zone-boundary phonons were used for the nonlinear least-squares fitting. In general, we obtained excellent agreement between the calculated and observed frequencies. The resulting parameters showed that the short-range interaction between the nearest titanium and oxygen is approximately 1 order of magnitude stronger than the interactions between the lead and oxygen or between the oxygens.The calculations showed that the lowest transverse-optic mode of E symmetry in ${\mathrm{PbTiO}}_{3}$ has eigenvectors similar to those predicted by Last, whereas in ${\mathrm{BaTiO}}_{3}$ the ionic movement in the lowest optic E mode can be approximated by the description of Slater. The phonon dispersion curves for various directions of the wave vector q were computed. These results are in good agreement with the inelastic neutron measurements by Shirane et al. A calculation of the oblique phonons near the zone center is presented and compared with the available experimental data. These calculations show that the long-range Coulomb forces dominate the anisotropic forces in these crystals. A theoretical approach for computing the elastic, dielectric, and piezoelectric properties is presented and the proposed model applied for calculating these constants. The results are compared with the experimental data where existed. Finally, a least-squares analysis of the observed phonons in ${\mathrm{PbTiO}}_{3}$ near the tetragonal-cubic phase-transition temperature was carried out to understand the influence of anharmonic forces and the mechanism of the phase transition in this crystal. In general, the variation in the parameters obtained is very small. This shows that the small anharmonic forces may be sufficient to explain the variation of frequencies with temperature.