  We investigate the standing kink modes of a cylindrical model of coronal
loops. The density is stratified along the loop axis and changes
discontinuously at the surface of the cylinder. The periods and mode profiles
are studies with their deviation from those of the unstratified loops. The aim
is to extract information on the density scale heights prevailing in the solar
corona. The problem is reduced to solving a single second-order partial
differential equation for $\delta B_z(r,z)$, the longitudinal component of the
Eulerian perturbations of the magnetic field. This equation, in turn, is
separated into two second-order ordinary, differential equations in $r$ and $z$
that are, however, connected through a dispersion relation between the
frequencies and the longitudinal wave numbers. In the thin tube approximation,
the eigensolutions are obtained by a perturbation technique, where the
perturbation parameter is the density stratification parameter. Otherwise the
problem is solved numerically.
