We report developments in the measurement of transverse elastic properties of a range of polymer fibres. The cylindrical fibre specimen is compressed across a diameter between a pair of parallel flat plates by a known load, while two quantities are measured; the width of the rectangular contact zone at one of the fibre-plate boundaries, and the degree of diametrical compression in the direction of the compressing force. Both measurements are used together With the relevant elastic solutions to give estimates of the transverse elastic modulus. For some fibres, plasticity is detected in the measurements of diametrical compression, and loading strategies are adopted to isolate this effect; the modulus values obtained from the two measurements are then in good agreement, provided the fibre is sufficiently large to permit accurate measurement of the contact zone. Finite-element modelling is used to show that the elastic-plastic behaviour is essentially understood and to estimate a value for yield stress. Results are presented for five fibres with diameters in the range 0.13-0.57 mm.