The performance of braided fiber-reinforced composites is determined by the braided structure, so yarn spatial arrangement prediction is a crucial step in the manufacturing process of fiber-reinforced composites. This study aims to predict fabric on arbitrary mandrels based on the yarn interactions, especially for mandrels with flat surfaces. An interaction yarn deposition model is proposed to simulate the process of braiding arbitrary-shaped mandrels. A dynamic deposition model is established at the moment of deposition, and a quasi-static equilibrium equation is added to determine the spatial position of yarn interaction points. Post-processing of positional information is performed to obtain the yarn spatial arrangement on the mandrel’s surface. Experiments were conducted using Zhongfu Shenying 12K T700 carbon yarn and Yunlu Composite 176-carrier radial braiding equipment. The experimental results show that the actual fabric exhibits an S-shaped distribution on the flat surface of the mandrel, matching the predicted results of the model.