Context. Observations of post-flare transversal coronal loop oscillations by TRACE have given us an excellent opportunity to implement magneto-seismological techniques for probing the plasma fine structure of the Sun's upper atmosphere.\ud Aims. We investigate the combined effect of magnetic and density stratification on transversal coronal loop oscillations.\ud Methods. A coronal loop will be modelled as an expanding magnetic flux tube with arbitrary longitudinal plasma density. The governing equation of the fast kink body mode is derived and solved by analytical approximation and numerical methods.\ud Results. It is found that even a relatively small coronal loop expansion can have a significant and pronounced effect on the accuracy of the plasma density scale height measurements derived from observation of loop oscillations.\ud Conclusions. To conduct more accurate and realistic magneto-seismology of coronal loops, the magnetic field divergence should be taken into account.\u
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