This machine comprises a hopper (2) for storing empty straws, a station (5) for filling the straws, and a transfer device (3), such as a rotary barrel, which is provided with notches for receiving and holding the straws (p) and with which straws removed from the hopper are conveyed to the filling station (5); it is designed to process at least two categories of straws of different diameters, notches being subdivided into at least two distinct series that can be used selectively, the elements (90) of one of the two series being designed to adapt to straws of large diameter, while the elements (91) of the other series are designed to adapt to straws of small diameter. Machine that can be used in more than one way in the packaging of semen for artificial insemination, particularly of cows.