The compressive and torsional buckling behavior of carbon nanotube bundles at room temperature is examined with classical molecular dynamics simulation. The critical compressive load and stiffness of a single carbon nanotube in the bundle are found to be similar to those of individual carbon nanotubes. However, the critical torsional moment and stiffness of a single carbon nanotube in the bundle are found to be higher than those of individual carbon nanotubes. In addition, this study demonstrates that van der Waals interactions between the nanotubes in the bundle significantly affect the critical compressive load of the nanotube bundle.