In this paper a calculation method is explained to predict the total number of fibres crossing a rectangular section. The largest part of the paper deals with the theoretical calculation of an orientation factor. The orientation factor is defined here as the average length of the projection on the longitudinal axis of all fibres crossing a section, divided by the fibre length. Once the orientation factor is found, a simple calculation gives the number of fibres crossing a crack. Since the proposed approach is to a large extent new, there is a need for verification with test results. For this reason a fibre counting was done on 107 Rilem beam specimens, involving different fibre types. The comparison with the calculated number of fibres shows that the model provides good predictions of the number of fibres crossing a section.