The single-walled carbon nanotubes (SWCNTs) under high internal pressure are studied by the constant-pressure molecular dynamics method. The results show that SWCNTs are suitable candidates for high pressure nanocontainer, and they can resist 30 GPa to 110 GPa internal pressure. We find that the ultimate internal pressure that nanotubes can sustain is mainly determined by the radius of the tube, and it is not sensitive to the tube chirality. The breaking of the nanotube induced by high internal pressure is mainly due to bond stretching rather than bond angle changing. An elastic model is used to explain the size-dependent ultimate internal pressure behavior for SWCNTs.