An orbital wrapping machine includes a rotatable wrapping wheel and a drive system, with one or more roll mounts arranged circumferentially around the wrapping wheel and each configured to rotatably support a roll of stretch film. Rotation of the wrapping wheel about an object causes the stretch film to be wrapped around the object. A tensioning system applies a frictional resistance to rotation of each roll of stretch film as the firm is drawn off each roll during rotation of the wrapping wheel. The tensioning system includes a friction material and an adjuster that is capable of urging the friction material against an outer surface of the roll of stretch film at different levels of pressure to adjust the frictional resistance of each roll of stretch film.