A semiconductor die package and a method of forming the same are provided. The semiconductor die package includes a package substrate and a semiconductor device disposed over the package substrate. A ring structure is disposed over the package substrate and laterally surrounds the semiconductor device. The ring structure includes a lower ring portion arranged around the periphery of the package substrate. Multiple notches are formed along the outer periphery of the lower ring portion. The ring structure also includes an upper ring portion formed on the lower ring portion. The upper ring portion laterally extends toward the semiconductor device, so that the inner periphery of the upper ring portion is closer to the semiconductor device than the inner periphery of the lower ring portion. An adhesive layer is interposed between the lower ring portion and the package substrate.