In this work, individual single-wall carbon nanotubes (i-SWCNTs) and their parent bundled material (b-SWCNTs) are investigated by means of high pressure Raman spectroscopy. Pressure application results in the broadening and intensity redistribution of the radial breathing modes (RBMs) in both materials. These changes are more pronounced in the case of bundled SWCNTs as it is also evident by the abrupt increase of the G + bandwidth at ~5.5 GPa, in contrast to the smoother pressure response of the individual tubes. Our experimental findings reflect the size dependent cross-section deformation of carbon nanotubes which evolves differently in the two materials investigated.