A machine for producing substantially cylindrical articles of the tobacco processing industry; each article comprises a tubular body; a container element, which is arranged in the area of a first end of the tubular body and has an end opening facing outwards, at least one side wall and a bottom wall opposite to said end opening; a substantially rigid element, partially housed inside the container element and having an end portion, which protrudes through said end opening to the outside of the container element; and loose material, which is arranged inside the container element between the substantially rigid element and the bottom wall; the machine comprising a conveyor which is adapted to move at least one container element containing the loose material along a given path through an insertion station and comprises at least one seat designed to house the container element and provided with at least one inner lateral surface adapted to be in contact with said side wall; an insertion assembly, which is designed to insert the respective substantially rigid element into the container element, is arranged in the area of the insertion station and comprises a pushing unit to push the substantially rigid element downwards through said end opening, so as to partially insert it into the container element; and contrast means to exert a resistance on the bottom wall which is opposite to the push exerted by the pushing unit; and a feeding assembly, which is adapted to feed the substantially rigid element to the insertion station and comprises a transfer device to move the substantially rigid element in a transverse direction relative to the direction in which the pushing unit pushes the substantially rigid element through said end opening; wherein the transfer device comprises a first and a second half-shell (56, 57), which are adapted to be coupled to one another so as to house the substantially rigid element between them, and actuating means to move the first and the second half-shell (56, 57). the machine comprising a conveyor which is adapted to move at least one container element containing the loose material along a given path through an insertion station and comprises at least one seat designed to house the container element and provided with at least one inner lateral surface adapted to be in contact with said side wall; an insertion assembly, which is designed to insert the respective substantially rigid element into the container element, is arranged in the area of the insertion station and comprises a pushing unit to push the substantially rigid element downwards through said end opening, so as to partially insert it into the container element; and contrast means to exert a resistance on the bottom wall which is opposite to the push exerted by the pushing unit; and a feeding assembly, which is adapted to feed the substantially rigid element to the insertion station and comprises a transfer device to move the substantially rigid element in a transverse direction relative to the direction in which the pushing unit pushes the substantially rigid element through said end opening; wherein the transfer device comprises a first and a second half-shell (56, 57), which are adapted to be coupled to one another so as to house the substantially rigid element between them, and actuating means to move the first and the second half-shell (56, 57).