  The Casimir energy of an infinite compact cylinder placed in a uniform
unbounded medium is investigated under the continuity condition for the light
velocity when crossing the interface. As a characteristic parameter in the
problem the ratio $\xi^2=(\epsilon_1-\epsilon_2)^2/ (\epsilon_1+\epsilon_2)^-2
= (\mu_1-\mu_2)^2/(\mu_1+ \mu_2)^2 \le 1$ is used, where $\epsilon_1$ and
$\mu_1$ are, respectively, the permittivity and permeability of the material
making up the cylinder and $\epsilon_2$ and $\mu_2$ are those for the
surrounding medium. It is shown that the expansion of the Casimir energy in
powers of this parameter begins with the term proportional to $\xi^4$. The
explicit formulas permitting us to find numerically the Casimir energy for any
fixed value of $\xi^2$ are obtained. Unlike a compact ball with the same
properties of the materials, the Casimir forces in the problem under
consideration are attractive. The implication of the calculated Casimir energy
in the flux tube model of confinement is briefly discussed.
