  The Casimir stress on a cylinderical shell in background of conformally flat
space-time for massless scalar field is investigated. In the general case of
Robin (mixed) boundary condition formulae are derived for the vacuum
expectation values of the energy-momentum tensor and vacuum forces acting on
boundaries. The special case of the dS bulk is considered then different
cosmological constants are assumed for the space inside and outside of the
shell to have general results applicable to the case of cylindrical domain wall
formations in the early universe.
