  We analyze the classical stability of Q-tubes --- charged extended objects in
$(3+1)$-dimensional complex scalar field theory. Explicit solutions were found
analytically in the piecewise parabolic potential. Our choice of potential
allows us to construct a powerful method of stability investigation. We check
that in the case of the zero winding number $n=0$, the previously known
stability condition $\partial^2E/\partial Q^2<0$ for Q-balls is fulfilled.
However, in the case $n\geq 1$, we find a continuous family of instabilities.
Our result has an analogy with the theory of superconductivity of the second
type, in which the vortex with $n>1$ becomes unstable towards the decay into
the $n$ vortices with the single winding number.
