A method for fabricating an organic electroluminescent display device including the steps of preparing first and second substrates, forming an organic electroluminescent display on the first substrate, forming a first etching mask film on an upper surface of the second substrate, forming a second etching mask film on a lower surface of the second substrate, performing a first etching process on the upper surface of the second substrate, forming a third etching mask film on an etched portion of the second surface of the glass substrate, performing a second etching process on the upper surface of the second substrate to form a plurality of grooves on the upper surface of the second substrate, removing the first and second etching mask films, the second etching film remaining on the etched portion of the second surface of the glass substrate, and encapsulating the organic electroluminescent display between the first and second substrates.