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