A　scheme　was　proposed　for　the　generation　of　maximally　entangled　field　states　in　multiple　cavities.　In　the　scheme　an　appropriately　prepared　ladder-type　multi-level　atom　is　sent　through　the　cavities　initially　in　vacuum　states.　After　resonant　interactions　the　cavity　system　is　prepared　in　a　highly　entangled　state　with　the　atom　left　in　its　lowest　state.