The nucleus pulposus of the intervertebral disc exerts a pressure which enables it to support axial compression when contained by the annulus fibrosus. The disc was modelled as a thick-walled cylindrical pressure vessel in which the nucleus was contained radially by the annulus. As a result, the stress in the annulus had radial (compressive) as well as tangential (tensile) components. The radial stress at a given point in the annulus was considered to be balanced by the internal pressure which is expected to arise from the attraction of water by proteoglycans. There was a reasonable agreement between the calculated radial stress distribution and published results on the distribution of water within the annulus. As the internal pressure is expected to be isotropic, the annulus was expected to contribute to the axial resistance to compression of the disc; this contribution would be equal, in magnitude, to the radial stress. Predictions of the pressure distribution within the annulus were similar to published experimental measurements made in the radial and axial directions. The tangential stress within the annulus was considered to arise from the restoring stress in its strained collagen fibrils.