We study the behaviour of the non-retarded van der Waals force between a planar substrate and a single-walled carbon nanotube, assuming that the system is immersed in a liquid medium which exerts hydrostatic pressure on the tubes surface, thereby altering its cross-section profile. The shape of the latter is described as a continual structure characterized by its symmetry index $n$. Two principle mutual positions of the tube with respect to the substrate are studied: when one keeps constant the minimal separation between the surfaces of the interacting objects; when the distance from the tubes axis to the substrates bounding surface is fixed. Within these conditions, using the technique of the surface integration approach, we derive an integral form of the expressions which give the dependence of the commented force on the applied pressure.
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