In this paper, the non-linear mechanical response of triaxial braided composites under multiple loading conditions was investigated with a meso-scale simulation strategy. Numerical predictions made by three-dimensional finite element unit cells with a realistic internal geometry in two nesting configurations correlated well with experimental stress–strain curves and damage mechanisms. Although the investigated braid topologies exhibited considerable geometric variability, the unit cell modelling approach with a compacted geometry model built from average input parameters was capable of correctly predicting the homogenised constitutive response, localisation, and damage evolution. Further, the mechanical response was predicted under variable uni-axial off-axis load cases and the effect of the textile topology on the ultimate strength of the material was investigated. Aside from providing a valuable insight into how damage propagation is affected by the meso-structure, the predicted stress–strain curves can be used to calibrate macroscopic material models suitable for large-scale crash simulations of textile composites.