A surgical stapling instrument comprises a frame having a body portion and a handle. A staple fastening assembly is provided in the distal region of the instrument and includes a cartridge device, which comprises at least one closed row (10, 12) of staples, and an anvil. The anvil is movable relative to the cartridge device and is adapted to cooperate with the cartridge device for forming the ends of the staples exiting from the cartridge device. A knife, which has a closed cutting edge, is contained within the cartridge device and is positioned such that there is at least one closed row (10, 12) of staples on the outside of the cutting edge. It can be moved towards the anvil. The line along which the closed row (10, 12) of staples is arranged has a stepped shape, leaving a plane perpendicular to the longitudinal axis of the staple fastening assembly, such that this line has a larger total length than the projection of this line onto this plane. This provides a greater flexibility of the anastomotic site and less tension during instrument removal, alleviating the incidence of clinical complications.