  We consider a model involving a self-interacting complex scalar field
minimally coupled to gravity and emphasize the cylindrically symmetric
classical solutions. A general ansatz is performed which transforms the field
equations into a system of differential equations. In the generic case, the
scalar field depends on the four space-time coordinates. The underlying
Einstein vacuum equations are worth studying by themselve and lead to numerous
analytic results extending the Kasner solutions. The solutions of the coupled
system are -static as well as stationnary- gravitating Q-tubes of scalar matter
which deform space-time.
