In the present paper, an explicit beam element for non-symmetric thin-walled composite shafts is developed. The element is developed from the WS element which normally demands numerical integration. It allows circumferential changes of the radius but takes advantage of the fact that it is only the second term in a Fourier series expansion that has a major influence on the dynamic behaviour of the rotor. The element allows transverse shear and moreover the mass is not distributed on the centre line.