  We report a Raman scattering study of polycrystalline CaCu$_3$Ti$_4$O$_{12}$
(CCTO) under pressure up to 5.32 GPa. The pressure dependence of several Raman
modes was investigated. No anomalies have been observed on the phonon spectra
thereby indicating that the T$_{h}$ (Im$\bar 3$) structure remains stable for
pressures up to 5.32 GPa. The pressure coefficients for the observed modes were
determined. This set of parameters was used for evaluating the stress developed
in CCTO thin films.
