A malleable, bioabsorbable polymeric staple includes a back span with two legs depending perpendicularly therefrom that are deformed toward each other initially and then upwardly toward the back span such that end points on each leg extends to the side and past the back span. The staple has a noncircular cross-sectional shape. A surgical staple-deforming anvil for deforming the staples has a staple-receiving face formed with a pair of elongated, non-collinear pocket-like depressions each having an entry end lying on a longitudinal axis parallel to the back span of the staple, and an exit end. The respective exit ends of the pocket depressions are located on opposite sides of the longitudinal axis. Accordingly, the legs of a staple driven toward the anvil and received in the pocket depressions are initially bent toward each other and then steered upwardly toward opposite sides of the back span.