This series of papers on ±55° filament-wound glass-fibre/epoxy-resin tubes consists of three parts. In the present paper (Part III), the macroscopic mechanical behaviour of the tubular structure is presented. A method for predicting composite tube macroscopic properties from the ply constants is given. A more general analytical method is used for determining ply stresses of a composite tube under a combined load, which will then be compared with 3D finite-element analysis, classical and adjusted laminate theory. Failure envelope prediction is then made according to the micro- and meso-scale model results. The stresses distribution in the tube thickness direction predicted by the present method agrees well with 3D finite-element analyses. Four methods give similar stress distribution results under tensile loading, but different ones under internal pressure loading. For failure envelope prediction, the first-ply-failure theory underestimates the failure load for pressure dominated loading. The effect of possible micro structural damage on the failure load prediction is also discussed and compared with experimental results. In Part I (Bai et al. Compos. Sci. Technol., 1997, 57, 141–153), the microstructure, mechanical behaviour and damage initiation mechanisms were presented. In Part II (Bai et al. Compos. Sci. Technol., 1997, 57, 155–164), micromechanical modelling of the damage initiation was conducted in order to determine the mechanical conditions under which different microcracking mechanisms occur.