A surgical stapling instrument suitable for performing a gastrointestinal anastomosis is provided. The stapling instrument incorporates a staple height adjusting mechanism which enables the gap between its jaw members to be adjusted to select different staple heights to be produced when the staples are formed. Preferably, the stapling instrument includes a pair of elongate jaw members, one of which supports a staple cartridge adapted to receive at least two laterally spaced longitudinal rows of staples, and the other provided with an anvil adapted to form the staples. A pusher bar and knife assembly slidable longitudinally relative to the jaw members sequentially drives the staples from the cartridge and forms the staples against the anvil to produce a pair of laterally spaced rows in the tissue. The pusher bar and knife assembly includes a knife blade for cutting the tissue along a line between the longitudinal staple rows. A set of jaw support members is carried by the knife blade which travel along the elongate jaw members as the pusher bar and knife assembly is advanced to provide local support to the jaw members. The angular orientation of the knife blade relative to the jaw members is adjustable by the staple height adjusting mechanism to vary the vertical spacing between the jaw support members as the gap between the jaw members is varied.