A machine for filling a sealed soft container (2) with fluid material in an aseptic condition comprises a sealing box (3) comprising two complementary half-boxes (4a & 4b) having respective sealing edges (21, 22, 23) that can be brought into mutual contact to isolate their interior from the outside environment when the complementary half-boxes (4a & 4b) are clamped together, vertical and horizontal blades located in the sealing box (3) for forming an aperture (5) in a portion of the container (2) inserted in the sealing box (3), filling device (8, 9) for filling the container (2) through the aperture (5), suckers (28a) for widening the aperture (5), and welding device (32) for sealing the aperture (5) on termination of filling.