A semiconductor die package and a method of forming the same are provided. The semiconductor die package includes a package substrate, an interposer substrate over the package substrate, semiconductor dies over the interposer substrate, and an underfill element over the interposer substrate and between the semiconductor dies and interposer substrate. The semiconductor die package also includes a ring structure and one or more lid structures separated from the ring structure. The ring structure is coupled to the package substrate to control warpage. The lid structures are coupled to the top surfaces of the semiconductor dies to control warpage and help heat dissipation. In addition, the lid structures define a gap to allow a portion of the underfill element between the adjacent semiconductor dies to be exposed, so that stress concentration on that portion can be avoided or reduced. Accordingly, the reliability of the semiconductor die package is improved.