Apparatus for wrapping a sheet of wrapping material around a rod-shaped article or around a plurality of linearly arranged substantially cylindrical segments, either of which comprising at least one fragile segment, the apparatus comprising - a rotatable drum having a central longitudinal axis and a circumferential drum surface, the circumferential drum surface comprising a plurality of flutes extending in a direction parallel to the central longitudinal axis of the drum, with each flute being adapted to hold within it a rod-shaped article or a plurality of linearly arranged substantially cylindrical segments, either of which comprising at least one fragile segment, the circumferential drum surface further comprising attachment portions arranged between the flutes, each attachment portion being adapted to hold a sheet of wrapping material against the respective attachment portion, with the sheet of wrapping material having an adhesive on an outer surface of the wrapping material facing away from the circumferential drum surface; the apparatus further comprising - a rolling device comprising a contact surface arranged at a predetermined distance from the circumferential drum surface, the predetermined distance being chosen such that the contact surface is to contact a periphery of the respective to-be-wrapped rod-shaped article or the to-be-wrapped plurality of linearly arranged substantially cylindrical segments in the respective flute in a manner to make the rod-shaped article or the plurality of linearly arranged substantially cylindrical segments move out of the flute and roll over the outer surface having the adhesive thereon of the sheet of wrapping material held on the adjacent attachment portion to wrap the sheet of wrapping material around the rod-shaped article or around the plurality of linearly arranged substantially cylindrical segments, the apparatus being characterized in that at least a portion of the contact surface is resiliently displaceable away from the circumferential drum surface so as to make the rod-shaped article or the plurality of linearly arranged substantially cylindrical segments move out of the flute. - a rotatable drum having a central longitudinal axis and a circumferential drum surface, the circumferential drum surface comprising a plurality of flutes extending in a direction parallel to the central longitudinal axis of the drum, with each flute being adapted to hold within it a rod-shaped article or a plurality of linearly arranged substantially cylindrical segments, either of which comprising at least one fragile segment, the circumferential drum surface further comprising attachment portions arranged between the flutes, each attachment portion being adapted to hold a sheet of wrapping material against the respective attachment portion, with the sheet of wrapping material having an adhesive on an outer surface of the wrapping material facing away from the circumferential drum surface; - a rolling device comprising a contact surface arranged at a predetermined distance from the circumferential drum surface, the predetermined distance being chosen such that the contact surface is to contact a periphery of the respective to-be-wrapped rod-shaped article or the to-be-wrapped plurality of linearly arranged substantially cylindrical segments in the respective flute in a manner to make the rod-shaped article or the plurality of linearly arranged substantially cylindrical segments move out of the flute and roll over the outer surface having the adhesive thereon of the sheet of wrapping material held on the adjacent attachment portion to wrap the sheet of wrapping material around the rod-shaped article or around the plurality of linearly arranged substantially cylindrical segments,