Thin-walled filament wound glass fibre reinforced tubes supported on a rigid flat plate were loaded laterally by a rigid spherical indenter. The finite element technique was used for the prediction of deformation and strains in the tube up to failure which occurred at high levels of indentation. The analysis made allowance for the large displacements. The tube wall material was modelled as a monolithic, orthotropic continuum. The theoretical results are compared with experimental data from tube indentation tests. Final failure is shown to be due to local axial shell buckling.