Reinventing concrete construction with textile-reinforced concrete, this innovative composite material allows engineers new possibilities for filigree, yet durable constructions in concrete. This work of research examines the bond behaviour of this new composite material, and in particular, the cause of longitudinal cracks which can occur in the textile-reinforcement layer of this concrete. Experimental and numeric examinations show that the magnitude of the splitting tensile forces, which lead to the aforementioned cracking, is largely dependent on the geometry of the individual fibre strands. In order to characterise the fibre strands, geometrical parameters were introduced, which were assigned to Laser Scans of textile reinforcements. Based on the evidence collected, a mechanical model, in which the input parameters are of geometric nature, was presented allowing calculation of the splitting tensile force. This method has made it possible to better understand the bond behaviour of textile reinforcements in concrete and has progressed the effort to establish this new material in construction.