Abstract: A bag (1) which includes at least two flexible but tearable walls (2, 3) placed opposite to one another, and a margin (4) for rigidly joining the two walls (2, 3) one against the other, disposed so as to delimit, on the one hand, the outer periphery (6 to 9) of the bag (1), and on the other hand, the outer contour (10 to 13) of a central volume (5) intended to contain a product which can be liquid, pasty or pulverulent, for example. There is a line (18) of weakest resistance which extends on the joining margin (4) and which is intended to allow the bag (1) to be opened by tearing the walls (2, 3). A first end (19) of the line of weakest resistance (18) is located at a peripheral edge (7) of the joining margin (4).