Single-walled carbon nanotubes show linear elasticity under hydrostatic pressure up to 1.5 GPa at room temperature. The volume compressibility, measured by in situ synchrotron x-ray diffraction, has been determined to be 0.024 GPa (-1). Theoretical calculations suggest that single-walled carbon nanotubes are polygonized when they form bundles of hexagonal close-packed structure and the intertubular gap is smaller than the equilibrium spacing of graphite (002) (d = 3.35 A). It has also been determined that the deformation of the trigonal nanotube lattice under hydrostatic pressure is reversible up to 4 GPa, beyond which the nanotube lattice is destroyed.