Abstract: In drawing glass fiber from a glass melting furnace to form a multiplicity of filaments which are first divided and formed into a plurality of strands which are then wound on a single spindle to form a plurality of square-ended packages thereon, the strands are shifted to a front waste take-up portion of the spindle by means of a guide which is moved from the rear end to the front end of the spindle across the paths of movements of the strands when the packages are fully wound, to enable the fully wound spindle to be replaced by a new spindle without interrupting the drawing of glass fiber. The spacing between the spindle and the path of travel of the guide and the speed of travel of the guide are set at a low level and a high level respectively which are sufficient to ensure at least loose portions of the strands, which are produced when they drop into the groove between the adjacent packages, to be immediately wound on the peripheral surface of the adjacent package.