Machine (1) for filling bags (100) with a granular product comprising a filling station (2). The machine comprises a supporting device (8) for supporting bags (100) below the filling station (2). The supporting device (8) comprises an assembled supporting surface (10) pivoting on a pivot shaft (12), and actuating means (18). The actuating means (18) are a motor the angular position of which is controlled by control means (32). The supporting surface (10) has a first end (14), arranged upstream of said filling station (2) in the forward movement direction of the bags, and a second end (16), arranged downstream of said filling station (2) in the forward movement direction of the bags. The supporting surface (10) can pivot in an alternating manner around said pivot shaft (12) for moving the base of the bag (100) which is located in the filling station (2) in operation during filling. The invention also relates to a method for filling said bag.