According to the invention, an apparatus is provided for extruding a medical instrument which can be inserted into a human or animal body. The apparatus comprises a device for supplying rod-shaped bodies, an extrusion device comprising a housing, said housing having a surrounding side wall which, at the frontward end as seen in the manufacturing direction, is provided with a nozzle wall comprising a discharge nozzle and, at the rearward end as seen in the manufacturing direction, is provided with a spindle sleeve. The space in the housing between the spindle sleeve, the side wall and the discharge nozzle delimits an extrusion space and the housing is provided with a polymer supply device in the area of the extrusion space. Further, a cannula device is provided which extends in the manufacturing direction and is designed to insert at least one rod-shaped body from the device for supplying rod-shaped bodies into the extrusion space in a predetermined spatial arrangement, which comprises at least one tubular cannula having a rearward supply end as seen in the manufacturing direction and a frontward discharge end as seen in the manufacturing direction, the cannula device being arranged approximately in straight alignment with respect to the discharge nozzle and extending through the spindle sleeve such that its discharge end situated in the manufacturing direction terminates at a distance from the discharge nozzle in the extrusion space.