Based on a theoretical model developed previously by the authors in Part II of this series for a single fibre pull-out test, a methodology for the evaluation of interfacial properties of fibre-matrix composites is presented to determine the interfacial fracture toughness G(c), the friction coefficient mu, the radial residual clamping stress q(0) and the critical bonded fibre length z(max). An important parameter, the stress drop Delta sigma, which is defined as the difference between the maximum debond stress sigma(d)* and the initial frictional pull-out stress sigma(fr), is introduced to characterize the interfacial debonding and fibre pull-out behaviour. The maximum logarithmic stress drop, In(Delta sigma), is obtained when the embedded fibre length L is equal to the critical bonded fibre length z(max). The slope of the In(Delta sigma)-L curve for L bigger than z(max) is found to be a constant that is related to the interfacial friction coefficient mu. The effect of fibre anisotropy on fibre debonding and fibre pull-out is also included in this analysis. Published experimental data for several fibre-matrix composites are chosen to evaluate their interfacial properties by using the present methodology.