We study the pull-in voltage characteristics of several multiwall nanotube electromechanical switches such as suspended carbon nanotubes over a graphitic ground lectrode. Electromechanical analysis has been performed by accounting for three coupled energy domains: elastostatics, electrostatics, and van der Waals interactions. We have shown that, by comparing to molecular dynamics simulations, the use of continuum theories for mechanics and van der Waals interactions is justified. The continuum approach proposed in this work has been used to simulate the behaviour of carbon-nanotube based nano-switches. Several cantilever and fixed-fixed carbon nanotubes over a graphite ground plane have been simulated. The pull-in voltage calculations for a cantilever switch and a fixed-fixed switch emphasize the significance of van der Waals forces in nanoelectromechanical switches.