  Single walled carbon nanotube's cross section can be flattened under
hydrostatic pressure. One example is the cross section of a single walled
carbon nanotube successively deforms from the original round shape to oval
shape, then to peanut-like shape. At the transition point of reversible
deformation between convex shape and concave shape, the side wall of nanotube
is flattest. This flattest tube has many attractive properties. In the present
work, an approximate approach is developed to determine the equilibrium shape
of this unstrained flattest tube and the curvature distribution of this tube.
Our results are in good agreement with recent numerical results, and can be
applied to the study of pressure controlled electric properties of single
walled carbon nanotubes. The present method can also be used to study other
deformed inorganic and organic tube-like structures.
