Casing for Battery and Battery

The present invention discloses a casing for a battery and the battery. The casing for the battery comprises a body. The body comprises a shell and at least one cover; at least one end of the shell is open; the cover is arranged at the one end of the shell; the shell comprises at least one first shell portion and a second shell portion which are connected to each other; the first shell portion is opposite to the cover; a thickness of the first shell portion is larger than that of the second shell portion; and a groove recessed toward a central axis direction of the shell is formed in the first shell portion.