The charge distribution on the surface of a biased nanotube freestanding above an infinite grounded plane is investigated. The relationship between the charge distribution and the geometry of the nanotube is examined in detail using full three dimensional numerical simulations based on the boundary element method (BEM). A model of the concentrated charge at the end of nanotubes is proposed. The charge distribution for a clamped cantilever nanotube is also computed and discussed. The findings here reported are of particular usefulness in the design and modeling of electrostatic actuated nanotube/nanowire based nano-electromechanical systems (NEMS).