A cushioning conversion machine (100, 200, 300, 400, 500, 600, 700, 800, 900) comprising a conversion assembly (101, 201, 301, 401, 501, 601, 701, 801, 901) which converts a sheet stock material into a three-dimensional strip of cushioning. The conversion assembly (101, 201, 301, 401, 501, 601, 701, 801, 901) includes a forming assembly (120, 220, 320, 420, 520, 620, 720, 820, 920) that forms the stock material into a strip of stock material. The forming assembly (120, 220, 320, 420, 520, 620, 720, 820, 920) comprises an external forming device (122, 222, 322, 422, 522, 622, 722, 822, 922) and an internal forming device (124, 224, 324, 424, 524, 624, 724, 824, 924). The internal forming device (124, 224, 324, 424, 525, 624, 724, 824, 924) includes interacting and/or mandrel portions (164, 264, 364, 464, 564, 664, 764, 864, 964) which internally interact with lateral portions of the strip of stock material to internally reshape the cross-sectional geometry of the strip.