In a method and apparatus for making an absorbent structure, an absorbent core and a wrapsheet are arranged in an unwrapped configuration with a first face of the absorbent core facing a first face of the wrapsheet, and with the absorbent core disposed laterally between laterally opposite side margins of the wrapsheet such that the side margins of the wrapsheet extend laterally outward beyond the side edges of the absorbent core. Gas is directed to flow over the first and second faces of the wrapsheet at the lateral side margins thereof in a direction which moves the lateral side margins of the wrapsheet from the unwrapped configuration around the side edges of the absorbent core and over at least a portion of the second face of the absorbent core to define a wrapped configuration of the wrapsheet.