The recently suggested swing interaction between fast magnetosonic and Alfven waves (Zaqarashvili & Roberts 2002a) is generalized to inhomogeneous media. We show that the fast magnetosonic waves propagating across an applied nonuniform magnetic field can parametrically amplify the Alfven waves propagating along the field through the periodical variation of the Alfven speed. The resonant Alfven waves have half the frequency and the perpendicular velocity polarization of the fast waves. The wavelengths of the resonant waves have different values across the magnetic field, due to the inhomogeneity in the Alfven speed. Therefore, if the medium is bounded along the magnetic field, then the harmonics of the Alfven waves, which satisfy the condition for onset of a standing pattern, have stronger growth rates. In these regions the fast magnetosonic waves can be strongly "absorbed", their energy going in transversal Alfven waves. We refer to this phenomenon as "Swing Absorption". This mechanism can be of importance in various astrophysical situations.