An electric storage cell has an electric storage element and a covering body. The covering body houses the electric storage element and has a metal layer with a first principal face on the electric storage element side and a second principal face on the opposite side, an internal resin layer made of resin laminated onto the first principal face, and an external resin layer made of resin laminated onto the second principal face, with a groove part formed on the second principal face side of the metal layer. The above structures provides a highly reliable electric storage cell, covering film, and electric storage module capable of releasing the rising internal pressure safely in the event of abnormality.