A wrapping machine for wrapping material around a load includes a wrapping unit to wrap a portion of the material around the load and a supplying unit to supply the material portion to the wrapping unit. The wrapping unit includes wrapping device to unwind the material portion from the supplying unit and wrap it around the load. The wrapping unit includes a supporting ring, rotating around a wrapping axis and provided with a plurality of wrapping rollers, and an unwinding arm having a first end rotatably fixed to the support ring and a second end supporting at least one unwinding roller to abut and guide the portion of material towards the load during wrapping. The unwinding arm is movable to move the unwinding roller to/from the load during wrapping.