Abstract: The present invention relates to an apparatus for unwinding a material web (19), for example a paper web, which is wound up on a core (18), for example a paper core.It is desirable to be able to reuse cores and remnant paper webs thereon separately. However, it is associated with relatively high costs to separate the paper web from the paper core.The separation of the paper web from the paper core or stripping of the paper core is effected, according to the present invention, under purely machine-controlled methods by means of an apparatus with a device (1) which is arranged to support the core (18) with the web (19) and to rotate the core (18) with the web (19) while retaining the core (18) with the web (19) in a position during unwinding of the web (19); and with first means (29) which are disposed to discontinue the rotational drive when the core (18) is empty, whereupon the core (18) rolls away from the apparatus (1) because of its own rotation.