The standing quasi-modes of the ideal MHD in a zero-$beta$ cylindrical magnetic flux tube that undergoes a longitudinal density stratification and radial density structuring is considered. The radial structuring is assumed to be a linearly varying de
nsity profile. Using the relevant connection formulae of the resonant absorption, the dispersion relation for the fast MHD body waves is derived and solved numerically to obtain both the frequencies and damping rates of the fundamental and first-overtone, $k=1,2$ modes of both the kink ($m=1$), and fluting ($m=2$) waves. Where $k$ and $m$ are the longitudinal and azimuthal mode numbers, respectively.
