A machine (1) for wrapping food products (P), e.g. ice cream products, comprises at least one reel holder arrangement (200) for supplying a web (10) of wrapping material from a reel (201) of rolled-up wrapping material. The reel holder arrangement (200) comprises a rotatable reel holder for holding the reel (201) such that reel holder is driven to rotate by the machine (1) drawing the web (10) from the reel (201), and a brake module (202) which operable to apply a brake force to a shaft of the reel holder. A control unit (20) is arranged to generate, based on a measured or otherwise known web infeed rate (S in ) of the machine (1) and a measured rotational speed (ω m ) of the reel holder, a control signal (C1) for operating the brake module (202) to set the brake force so as to control tension in the web (10). The machine (1) may be a multi-lane wrapping machine with a plurality of reel holder arrangements (200).