The focus of this study is the development of a computational model with damage to predict failure of carbon fiber/epoxy filament wound composite tubes under radial compressive loading. Numerical analysis is performed via Finite Element Method (FEM) with a damage model written as a UMAT (User Material Subroutine) and linked to commercial software. The experimental analysis carried out followed ASTM D2412-11, where the specimen is parallel-loaded by two steel-based plates. Three stacking sequences have been evaluated. Both numerical and experimental results show that the presence of hoop layers at inner and outer layers plus ±75° non-geodesic layers gives maximum compressive load to the composite tube, since the reinforcement is wound closer to the loading direction. Moreover, failure modes are predominantly delaminations, which are confirmed via numerical analyses through high in-plane shear stresses levels, and via experimental analyses through stereoscopic micrographs.