  A class of exact general relativistic rotating thick disks surrounded by
rotating dust is constructed by applying the ``displace, cut, fill and
reflect'' method on the van Stockum class of metrics. Two particular solutions
are considered in detail. We find that the disks have annular regions with
negative energy density and heat flow is present in most of the radial
extension of the disk. It is shown that thin disks are composed of exotic
matter with an equation of state of cosmic strings or struts. We also comment
the recent relativistic galactic model proposed by Cooperstock and Tieu and the
presence of an additional disk of exotic matter in their model.
