Abstract The tensile properties and damage mechanisms observed in three‐dimensional four‐directional (3D4d), three‐dimensional five‐directional (3D5d) and three‐dimensional six‐directional (3D6d) braided composites (BCs) have been studied experimentally and numerically. Finite element (FE) models have been established using a continuous damage mechanics methodology and subsequently validated by comparing the results of the simulations with experimental data. The proposed method is then used to predict the tensile properties and damage propagation in these 3DBCs. The results show that the tensile strength of 3D4dBCs and 3D5dBCs is remarkably similar, but the 3D5dBCs have a greater tensile modulus. In contrast, the 3D6dBCs exhibit the lowest values for each of these test parameters. The FE models revealed the internal damage process of these 3DBCs. It has been discovered that the braiding, axial, and warp yarns have a significant influence on the fracture propagation path. In the 3D4dBCs, the damage mainly expands along the braiding yarn, eventually resulting in a fracture along the braiding angle. Under the influence of the axial yarns, which direct the evolution of damage along them, the failure patterns observed in the 3D5dBCs are longitudinal cracking. The failure modes identified in the 3D6dBCs are characterized by fracture along the transverse direction, primarily due to the abrupt failure of the warp yarns during initial loading. Highlights Established parametric FE models for 3D4d, 3D5d, and 3D6d braided composites. The mechanical properties and damage mechanisms of composites are compared. The effect of different yarns on the mechanical behavior in composites is studied.