Damage initiation is an important issue to understand the mechanical behavior of ceramic matrix composites. In the present work, a braided SiC/SiC composite tube was studied by FFT simulation tightly linked with micro-computed tomography (µCT) observations performed during an in situ uniaxial tensile test, which provide both the real microstructure, with a good description of local microstructural geometries, and location of cracks at the onset of damage. The FFT method was proven applicable to tubular structures and efficient to complete the large-scale simulation on a full resolution µCT scan (~6.7 billion voxels) within a short time. The edge effect due to the numerical periodic boundary conditions prescribed on the real and not rigorously periodic microstructure was quantified. The obtained stress field was compared to the cracks detected by the in situ µCT observations of the same composite tube. This one-to-one comparison showed that cracks preferentially initiated at tow interfaces, where sharp edges of macropores are mostly located and generate stress concentrations.