There are observational evidences for the existence of twisted magnetic field in the solar corona. Here, we investigate resonant absorption of propagating kink magnetohydrodynamic (MHD) waves in magnetic flux tubes with a continuous and twisted magnetic field. To this aim, we solve the linearized MHD equations in the limit of long wavelengthes. We show that for a given longitudinal wavenumber, frequency of propagating kink MHD waves is a monotonic function of the magnetic twist even when the azimuthal component of the magnetic field changes its sign. For the flux tube parameters considered in this paper, rapid damping of the kink waves reported in the observations occurs where the twist parameter and longitudinal wavenumber have opposite signs.
