A theoretical model including the effect of plasticity of the coating material on the single-fibre pull-out test has been developed. Both hardening and perfectly plastic coatings were modelled and the calculations have provided much information on the debond and maximum pull-out stresses. For both SiC fibre-glass and carbon fibre-epoxy systems, a stiff coating reduces substantially the partial debonding stress, but a soft coating increases it markedly. Although a higher coating yield stress increases the partial debonding stress slightly, the maximum pull-out stress is independent of the coating.