A surgical stapling instrument (1) comprises a body portion (2, 3), a handle (4) and a staple fastening assembly (8). The staple fastening assembly (8) includes a curved cartridge (10), which comprises at least one curved open row of staples, and a curved anvil (22), which is adapted to cooperate with the cartridge (10) for forming the ends of the staples exiting from the cartridge (10). The staple fastening assembly (8) is adapted to allow unobstructed access towards the concave inner faces of the cartridge (10) and the anvil (22). The cartridge (10) can be moved towards the anvil (22) from a spaced position for positioning tissue therebetween to a closed position for clamping the tissue. Preferably, a knife is contained within the cartridge (10) and is positioned such that there is at least one row of staples on at least one side of the knife.