A surgical stapler is provided. The stapler employs circumferential channels through which staples are deployed along an arc pathway against an anvil surface. The curved channels allow staples with relatively longer legs to be used in the stapler having a smaller diameter at the jaws. Also, by utilizing a curved path, a much larger staple can be placed in the same diameter device. Specialized curved staples for use with the stapler of the present invention are also provided. To further enable the benefits of the stapler with circumferential channels and method of staple deployment, novel jaw reinforcement structures are provided in the present invention. The jaw reinforcement structures are located towards the center or bladeline of the device instead of around the circumference as in conventional staplers, thereby clearing the outer area near the circumference of the device to provide room for longer staples and staple firing components.