We report our high-pressure Raman studies on single-wall carbon nanotube bundles carried out up to 25.9 GPa. The intensity of the radial modes decreases more drastically as compared to that of the tangential modes. The former could be followed up in pressure runs to 3 GPa. The most intriguing observation is the anomalous pressure behaviour of the 1594 cm(-1) tangential mode between 10 and 16 GPa. This feature, as well as the pressure dependence of intensity, peak position and linewidth, are reversible on decompression. The anomalous pressure dependence is argued to be associated with faceting of the tubes in the bundle, showing their remarkable resilience.