A method of making disposable, flexible containers for fluent products, the method comprising: forming a partially completed container blank comprising a flexible inner sheet and a flexible outer sheet, which together form a layered structure that comprises: a first layer, which is an outer layer of the layered structure, and is formed by a portion of the flexible outer sheet; a second layer, which is an inner layer adjacent to and in contact with the first layer, and is formed by a portion of the flexible inner sheet; a third layer, which is an inner layer, and is formed by a portion of the flexible inner sheet; and a fourth layer, which is an outer layer of the layered structure, and is formed by a portion of the flexible outer sheet; opening the partially completed container blank by separating a portion of the first layer from a portion of the second layer, wherein the opening comprises: bending portions of the second, third, and fourth layers toward a first direction; and dosing the partially completed container blank, by adding an expansion material out of a dispenser and into a space disposed between a portion of the first layer and a portion of the second layer; said method being characterized in that the bending toward the first direction comprises pushing on the second layer with one or more mechanical projections, each of which is inserted through an opening in the first layer, wherein the one or more mechanical projections are preferably disposed within a vacuum block that is pulling on the first layer. forming a partially completed container blank comprising a flexible inner sheet and a flexible outer sheet, which together form a layered structure that comprises: a first layer, which is an outer layer of the layered structure, and is formed by a portion of the flexible outer sheet; a second layer, which is an inner layer adjacent to and in contact with the first layer, and is formed by a portion of the flexible inner sheet; a third layer, which is an inner layer, and is formed by a portion of the flexible inner sheet; and a fourth layer, which is an outer layer of the layered structure, and is formed by a portion of the flexible outer sheet; a first layer, which is an outer layer of the layered structure, and is formed by a portion of the flexible outer sheet; a second layer, which is an inner layer adjacent to and in contact with the first layer, and is formed by a portion of the flexible inner sheet; a third layer, which is an inner layer, and is formed by a portion of the flexible inner sheet; and a fourth layer, which is an outer layer of the layered structure, and is formed by a portion of the flexible outer sheet; opening the partially completed container blank by separating a portion of the first layer from a portion of the second layer, wherein the opening comprises: bending portions of the second, third, and fourth layers toward a first direction; and dosing the partially completed container blank, by adding an expansion material out of a dispenser and into a space disposed between a portion of the first layer and a portion of the second layer; said method being characterized in that the bending toward the first direction comprises pushing on the second layer with one or more mechanical projections, each of which is inserted through an opening in the first layer, wherein the one or more mechanical projections are preferably disposed within a vacuum block that is pulling on the first layer.