A circular weaving machine (1, 1′) has warp-tape guide elements (2) which are arranged around a circular reed (4, 4′) in order to supply a multiplicity of warp tapes (3). Weaving-shed forming devices (5) group the fed warp tapes into two warp-tape groups (10, 11) and impart thereon mutually opposed alternating movements, with the result that a weaving shed (9) is opened and closed between the two warp-tape groups. A weaving shuttle (12) moves on an orbit in the opened weaving shed (9) and, in the process, introduces a weft tape from a weft-tape bobbin (13) carried thereby into the weaving shed (9), with the result that a fabric is formed. The fabric is drawn off through a weaving ring (15). The weaving shuttle (12) keeps the bobbin axis (13a) of the weft-tape bobbin (13) at an angular position which deviates by at most +/−15°, preferably at most +/−10°, from a normal to a surface (9a, 9a′) which contains the geometric connecting lines between the warp-tape guide elements (2) and the weaving ring (15).