A machine for wrapping a load with a film made of synthetic plastics includes a first frame suitable for supporting second frame that rotatably supports around, and slidably parallel to, a wrapping axis at least one wrapping unit including a reel of the film and a roller assembly arranged for unwinding and prestretching the film. The second frame is slidably mounted on the first frame and is movable along an advancing direction that is transverse, and in particular orthogonal, to the wrapping axis. A conveyor is provided for moving the load along the advancing direction. The conveyor and the second frame are movable in a mutually coordinated manner to wrap the load with the film also while the load is moved along the advancing direction.