The invention relates to a winding device (10) for producing a lap roll (12), in which the lap (14) is wound on a tube (H) driven by a circulating and continuous belt (18). The tube is arranged to be rotatable about a fixed axis (A) in a loop (20), formed between two guide pulleys (R1, R2), of the belt stretched by tensioning means (22). The tube which can be rotated about a fixed axis (A), and the two guide pulleys (R1 and R2) are dimensioned and arranged in relation to each other such that at the start of winding the loop (20) surrounds the tube (H) at an initial minimal angle of wrap of 120 DEG or more and preferably of 180 DEG or more. To produce a tension force dependent on the roll diameter, the tensioning means (22) is linked to control means (28).