A surgical stapling instrument (1) comprises a staple fastening assembly (4) in the distal region of said instrument, the staple fastening assembly (4) including a cartridge device (8) which comprises at least one closed row (17, 18) of staples and defines a wavy distal end surface (14), and an anvil (9) which defines a wavy proximal staple forming surface (20) substantially matching the distal end surface (14) and which is adapted to cooperate with the cartridge device (8) for forming the ends of the staples exiting from the cartridge device (8), wherein the distal end surface (14) and the staple forming surface (20) have a globally wavy shape including two opposite peaks (21) and two opposite valleys (22) angularly spaced at about 90° from the adjacent peaks (21) and in that said two-peaks-two-valleys wavy shape is formed by a stepped configuration of said surfaces (14, 20).