Carbon nanotubes (CNTs) have a unique combination of physical and mechanical properties, which makes them attractive for a number of applications. Investigation of the mechanical response of a CNT bundle under conditions of plane strain (uniaxial and biaxial lateral compression), since it can be used as an elastic damper for vibration and shock protection. In this work, using a chain model with a reduced number of degrees of freedom, the behaviour of a CNT bundle under uniaxial lateral compression is investigated. Quasistatic loading is used to calculate the elastic constants of the bundle. Dynamic loading reveals the propagation of shock waves of two types: the faster one propagates with the speed of longitudinal sound and causes insignificant deformation of the CNT cross sections, while the second one propagates approximately three times slower and leads to the collapse of the CNTs.