Abstract: A tape application device (1) comprises a tube holder (9), a roll retainer (11), guide means (35) for guiding a tape (3) from the inside (7a) of a roll (7) to the outside of a tube (5) and displacement means for rotating around an imaginary axis and translating in the direction of the imaginary axis the tube holder, roll retainer and guide means relative to each other, such that the tape is pulled out of the roll on the inside and is helically wound on the outside of the tube. The roll retainer (11) has support means (26) which support the roll only on the outside, which support means are formed by suction cups (27). The guide means (35) are formed by a resilient helical tape guide (37) which, during operation, resiliently pushes with one end (37a) against the inside (7a) of the roll (7) and with the other end (7b) is present close to the tube (5).