The phonon instabilities of cesium related to its pressure-induced $\mathrm{bcc}\ensuremath{-}\mathrm{to}\ensuremath{-}{\mathrm{fcc}}^{(1)}\ensuremath{-}\mathrm{to}\ensuremath{-}{\mathrm{fcc}}^{(2)}$ phase transitions are studied using the density-functional perturbation theory. It is found that at low pressure, both the bcc and fcc Cs are dynamically stable, but fcc is thermodynamically metastable. The high-pressure phase transitions of Cs from bcc to ${\mathrm{fcc}}^{(1)}$ and from ${\mathrm{fcc}}^{(1)}$ to ${\mathrm{fcc}}^{(2)}$ are related to the phonon instabilities of the long-wavelength acoustic modes resulted from the negative tetragonal shear elastic constant ${C}^{\ensuremath{'}}=\frac{1}{2}{(C}_{11}\ensuremath{-}{C}_{12}).$ During the ${\mathrm{fcc}}^{(1)}\ensuremath{-}\mathrm{to}\ensuremath{-}{\mathrm{fcc}}^{(2)}$ phase transition, all the phonon modes become soft, making it the most striking feature of this isostructural phase transition.