This study examines torsional vibration of Single-walled carbon nanotubes (SWCNTs) subjected to initial compression stresses. The nanotube structures are treated within the multilayer thin shell approximation with the elastic properties taken to be those of the graphene sheet. Simplified Flügge shell equations of motion are proposed as the governing equations of vibration for the carbon nanotubes. A new equation of motion and phase velocity of torsional waves propagating in carbon nanotubes (CNTs) subjected to initial compression stresses have been derived. The study reveals that the initial stresses present in the tube has a notable effect on the propagation of torsional waves. The results has been discussed and shown graphically. This investigation is very significant for potential application and design of nanoelectronics and nanodevices.