An organic electroluminescent (EL) display device includes an organic EL element formed on a substrate. The organic EL element includes a lower electrode, an organic EL layer and an upper electrode that are sequentially stacked on the substrate. A flat panel is attached to the substrate to encapsulate the organic EL element. At least one through hole is formed in the organic EL display device so as to allow gas inside the organic EL display device to flow out during an encapsulation process. A cap is provided to shut the one or more through holes.