A rigorous theory describing the diffraction of light by a muscle fibre has been formulated. The basis of this analysis is the rigorous coupled-wave approach of T. K. Gaylord & M. G. Moharam (Proc. IEEE 73, 894 (1985)); however, we obtain here a closed-form analytical result that is both mathematically simple and physically easy to understand. We have compared our results on striated muscle fibres with the analytical results obtained by A. F. Huxley (Proc. R. Soc. Lond. B 241, 65 (1990)) using the normal mode approach, and with those obtained by R. A. Thornhill, N. Thomas & N. Berovic (Eur. Biophys. J. 20, 87 (1991) using a multiwave first-order coupled-wave approximation. For an equivalent set of assigned fibre parameters, our results are consistent with these mentioned. Extension of this analysis to a fibre with different structures showed that the differences in diffraction efficiencies of different orders for a frog skeletal fibre and for an insect flight fibre are clear; the sensitivity to distinct structural organization of the fibre is very good.