Machine comprising at least one feed unit configured to automatically feed a plurality of tubular elements, preferably made of paper, toward a plurality of working units of said tubular elements, to make straws, preferably made of paper, wherein said plurality of working units comprises: (i) a bending unit, configured to carry out at least one bend on each of said tubular elements, preferably in correspondence with said bellows; (ii) a packaging unit, configured to package each of said straws, characterized in that said plurality of working units further comprises: (iii) a deformation unit, configured to make at least one bellows on each of said tubular elements so as to be present in each of said straws; wherein said deformation unit, said bending unit and said packaging unit are disposed in sequence and without a break in continuity with respect to an advancement direction of said tubular elements, so that the packaging of said folded straws occurs without interruption after said deformation unit has made the bellows and said bending unit has carried out the bending in correspondence with said bellows, and wherein said deformation unit, said bending unit and said packaging unit each comprise a cylindrical member (51, 76, 87), each cylindrical member (51, 76, 87) being rotatable around a respective axis of rotation (X3, X4, X5) at the same peripheral speed, wherein said units (19, 20, 21) are disposed so that said cylindrical members (51, 76, 87) are tangent to each other, and wherein each cylindrical member (51, 76, 87) has a peripheral surface (56, 79, 90) provided with retaining means of the straws suitable to support and temporarily retain the straws being formed, disposed parallel to said axis of rotation (X3, X4, X5), and angularly equidistant, from the adjacent straw, by a determinate pitch. (i) a bending unit, configured to carry out at least one bend on each of said tubular elements, preferably in correspondence with said bellows; (ii) a packaging unit, configured to package each of said straws, characterized in that said plurality of working units further comprises: (iii) a deformation unit, configured to make at least one bellows on each of said tubular elements so as to be present in each of said straws; said deformation unit, said bending unit and said packaging unit are disposed in sequence and without a break in continuity with respect to an advancement direction of said tubular elements, so that the packaging of said folded straws occurs without interruption after said deformation unit has made the bellows and said bending unit has carried out the bending in correspondence with said bellows, and wherein said deformation unit, said bending unit and said packaging unit each comprise a cylindrical member (51, 76, 87), each cylindrical member (51, 76, 87) being rotatable around a respective axis of rotation (X3, X4, X5) at the same peripheral speed, wherein said units (19, 20, 21) are disposed so that said cylindrical members (51, 76, 87) are tangent to each other, and wherein each cylindrical member (51, 76, 87) has a peripheral surface (56, 79, 90) provided with retaining means of the straws suitable to support and temporarily retain the straws being formed, disposed parallel to said axis of rotation (X3, X4, X5), and angularly equidistant, from the adjacent straw, by a determinate pitch.