The influence of an internal distribution of strain on the exciton reflection spectra is investigated. The resulting fluctuating optical constants give rise to a fluctuating phase of reflectivity. The standard deviation σ of these phase fluctuations is the quantity which can be observed, for example, between crossed polarizers or from ellipsometric measurements. Assuming the phase fluctuations to obey a Gaussian distribution, σ can be expressed in a simple way in terms of the degree of polarization or the depolarization of the reflected light. σ is then derived in terms of the standard deviations of the fluctuating strain components for wurtzite-structure crystals. To do this it is necessary to find the behavior of the six independent (complex) photoelastic coefficients in the excitonic resonance region. A simple approximation makes it possible to obtain these. Furthermore, it is necessary to derive the dependence of the phase of reflectivity on the direction of the fluctuating optical axis. The results obtained for σ are compared with the experimental depolarization spectra of ZnO. The only fitting parameter is the common standard deviation of the strain components. It is found that the fluctuating strain can reproduce the positions and relative magnitudes of the resonant depolarization peaks, but fails to reproduce the background level of depolarization and the magnitude of the A peak in one geometry.