It is shown by the method of molecular dynamics using a chain model that a multilayer packaging of identical single‐walled carbon nanotubes with a diameter of
D
>
2.5
nm located on a flat substrate is a multistable system. The system has many stationary states, which are characterized by the portion of collapsed nanotubes. The thickness of the package monotonically decreases with an increase in the portion of such nanotubes. For nanotubes with a chirality index (60,0), depending on the portion of collapsed nanotubes, the thickness of the 11‐layer package can vary from 12 to 36 nm. All stationary states of the package are stable to thermal fluctuations at
T
=
300
K. The transverse compression of the package is not elastic; due to the collapse of a part of the nanotubes, it only transfers the package from one stationary state to another with a smaller thickness.