The standing magnetohydrodynamic (MHD) modes in a cylindrical incompressible magnetic flux tube modelled as a straight core surrounded by a magnetically twisted annulus, both embedded in a straight ambient external field, are considered. The dispersion relation for the MHD waves is derived and solved numerically to obtain the frequencies of both the kink (m = 1) and fluting (m = 2, 3) waves. Damping rates due to both viscous and resistive dissipations in the presence of the twisted magnetic field are derived and solved numerically for both the kink and fluting waves.