An organic light emitting display device, a method of manufacturing an organic light emitting display device, and encapsulation structure for an organic light emitting display device are provided. The encapsulation structure includes a first porous layer, a first planarization layer, and a first barrier layer. The first porous layer above a substrate may have a curved top surface. The first planarization layer on the first porous layer may have a flat top surface. The first barrier layer on the first planarization layer may include a low melting point glass.