Mechanical response of the carbon nanotube bundle to uniaxial and biaxial lateral compression followed by unloading is modeled under plane strain conditions. The chain model with a reduced number of degrees of freedom is employed with high efficiency. During loading, two critical values of strain are detected. Firstly, period doubling is observed as a result of the second order phase transition, and at higher compressive strain, the first order phase transition takes place when carbon nanotubes start to collapse. The loading-unloading stress-strain curves exhibit a hysteresis loop and, upon unloading, the structure returns to its initial form with no residual strain. This behavior of the nanotube bundle can be employed for the design of an elastic damper
