The effects of elliptic shape of the coronal loop on the resonant absorption is studied. To do so, a typical coronal loop is modeled as a straight, zero-beta, nonaxisymmetric and longitudinally stratified cylindrical magnetized flux tube. We developed the connection formulae introduced by previous studies, for the case of elliptical shape tubes. Using the connection formulae, the dispersion relation is derived and solved numerically to obtain the frequencies and damping rates of the fundamental and first-overtone modes of fast kink body waves due to the resonant absorption. Our numerical results show that the elliptic shape of the loop alters the frequencies and damping rates of the tube as well as the ratio of frequencies of the fundamental and its first-overtone modes.
