The Casimir effect due to conformally coupled bulk scalar fields on background of conformally flat brane-world geometries is investigated. In the general case of mixed boundary conditions formulae are derived for the vacuum expectation values of the energy–momentum tensor and vacuum forces acting on boundaries. The special case of the AdS bulk is considered and the application to the Randall–Sundrum scenario is discussed. The possibility for the radion stabilization by the vacuum forces is demonstrated
