  The effects of both elliptical shape and stage of emergence of the coronal
loop on the resonant absorption of standing kink oscillations are studied. To
do so, a typical coronal loop is modeled as a zero-beta longitudinally
stratified cylindrical magnetic flux tube. We developed the connection formulae
for the resonant absorption of standing transversal oscillations of a coronal
loop with an elliptical shape, at various stages of its emergence. 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 kink modes. Our numerical results show that both the elliptical
shape and stage of emergence of the loop alter the frequencies and damping
rates of the tube as well as the ratio of frequencies of the fundamental and
its first-overtone modes. However, the ratio of the oscillation frequency to
the damping rate is not affected by the tube shape and stage of its emergence
and also is independent of the density stratification parameter.
