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Because of the decisive role of tow orientation in braided fabric on the mechanical performance of composite, having an accurate tow orientation prediction method for each specific mandrel shape is a cornerstone for applying circular braiding technology. This work presents a numerical method to predict the tow orientation on an irregular, constant cross-section mandrel. In this numerical method, the cross-section of the mandrel is approximated by a series of line segments, and then the surface meshes of the mandrel are generated in STL format. A set of kinematic equations, which was deduced from the simultaneous motion relationship between the translation of the take-up device and the rotation of the spools, was used to calculate the sequence of the deposition points located on the edges of surface mesh for the approximated tow orientation. Braiding experiments for various process parameters were conducted on a mandrel with a specially designed cross-section manufactured using a three-dimensional printer and the angle of the braiding tow was measured. The influence of translation speed, shape of cross-section and convergence region length on braiding angle were analysed via a comparison of the simulation results and the experimental data. Two types of variation of the braiding angles in the braided fabric and its influence factors are also discussed in detail. It was shown that the numerical method, which can rapidly predict the braiding angle for an irregular, constant cross-section mandrel, is beneficial for optimizing the process parameters for hollow composite component manufacture. [ABSTRACT FROM AUTHOR]