The stationary states of multi-walled carbon nanotubes are investigated. Numerical simulation has shown that for sufficiently large diameters, nanotubes become bistable systems. Regardless of the interaction with the substrates, they can be in two stable states: in an open, having an internal cavity, and in a collapsed state. The interaction with the flat substrate leads to the flattening of the nanotube, which makes its transition to the collapsed state energetically more favorable (the stronger the interaction, the more advantageous is the transition). It is shown that the change of the shape of a multilayer nanotube due to its interaction with the substrate or due to its collapse leads to a sharp increase in the number of its collective eigenmodes, in which all its layers already take part. The energy profile of the transition between the stationary states of the nanotube is obtained. This profile is a highly asymmetric double-well potential, with the first narrow minimum corresponding to the collapsed state, and with the second wide minimum corresponding to the open state of the nanotube.