Wrapping machine for wrapping a film around a load comprising an unwinding unit of said film, said unwinding unit and said load being rotatable relative to one another around a winding axis, said wrapping machine comprising: - first arm means movable to a first operating position in which said first arm means is adjacent to and facing a wall of said load and parallel to said winding axis so that at least one film strip is wrapped around said first arm means, said first arm means comprising first gripping means and cutting means respectively to grip and to cut said film at the end of a wrapping process of said load; - second arm means movable to a second operating position, in which said second arm means is parallel to and facing said first arm means, which is arranged in said first operating position, said second arm means comprising second gripping means movable for gripping a film portion of a terminal film section, which is comprised between said load and said unwinding unit, and for narrowing said film portion in the form of a pleated strip and then transferring said film portion to said first gripping means in order to allow said cutting means to cut said film portion and obtain a first end flap of the film held by said first gripping means and a second end flap of the film held by said second gripping means; - third arm means movable to a third operating position, in which said third arm means is parallel and adjacent to said first arm means, arranged in said first operating position, and to said second arm means, arranged in said second operating position, in order to divert said terminal film section so as to allow said second gripping means to grip said film portion irrespective of a size and/or a position of said load; said first arm means being movable so as to disengage from said film strip in order to insert and then release said a first end flap of the film between said film strip and said wall of the load. - first arm means movable to a first operating position in which said first arm means is adjacent to and facing a wall of said load and parallel to said winding axis so that at least one film strip is wrapped around said first arm means, said first arm means comprising first gripping means and cutting means respectively to grip and to cut said film at the end of a wrapping process of said load; - second arm means movable to a second operating position, in which said second arm means is parallel to and facing said first arm means, which is arranged in said first operating position, said second arm means comprising second gripping means movable for gripping a film portion of a terminal film section, which is comprised between said load and said unwinding unit, and for narrowing said film portion in the form of a pleated strip and then transferring said film portion to said first gripping means in order to allow said cutting means to cut said film portion and obtain a first end flap of the film held by said first gripping means and a second end flap of the film held by said second gripping means; - third arm means movable to a third operating position, in which said third arm means is parallel and adjacent to said first arm means, arranged in said first operating position, and to said second arm means, arranged in said second operating position, in order to divert said terminal film section so as to allow said second gripping means to grip said film portion irrespective of a size and/or a position of said load;