An exact theoretical treatment is given for propagation of light through an idealized representation of a striated muscle fibre. It leads to the following conclusions, of which only the first is expected on simple theory. 1. With normal incidence, the intensity of the first-order diffracted beams varies cyclically with the thickness of the fibre, being zero at thicknesses that are multiples of around 25 $\mu $m. 2. The same is true of first-order Bragg angle reflection, the diffracted intensity being zero at multiples of around 100 $\mu $m. 3. Even when the widths of A and I bands are equal, there is appreciable intensity in the second-order diffracted beams. 4. Even if neither A nor I bands are birefringent, the undiffracted component of the transmitted light shows negative birefringence, which is related to form birefringence. 5. When (as in real muscle) the A bands are birefringent and have a higher mean refractive index than the I bands, the waveguide action of the A bands causes the observed birefringence to be greater than the mean of A and I birefringence weighted according to the band widths. The main limitation of the theory is that it is not easily extended to take account of irregularities in the striation pattern such as are found in real muscle fibres.