A machine for filling bags with a granular product includes a filling station. The machine further includes a supporting device for supporting bags below the filling station. The supporting device includes an assembled supporting surface pivoting on a pivot shaft, and actuating means. The actuating means are a motor the angular position of which is controlled by control means. The supporting surface has a first end, arranged upstream of said filling station in the forward movement direction of the bags, and a second end, arranged downstream of said filling station in the forward movement direction of the bags. The supporting surface can pivot in an alternating manner around said pivot shaft for moving the base of the bag which is located in the filling station in operation during filling. A method for filling said bag can also be employed.