We present a macroscopic model for the behavior of smectic A liquid single crystal elastomers (LSCEs) under an external dilatory stress thus investigating the elastomeric analogue of the undulation instability in low molecular weight (LMW) smectic A liquid crystals. We show that the critical wavelength i C of the expected undulation pattern is given by an expression quite similar to that obtained for LMW smectic A phases. This result provides a possible explanation for the strong light scattering (high turbidity) observed by Nishikawa et al. very recently in thick samples of a smectic A LSCE above a certain threshold stress applied parallel to the layer normal in the experiments. We find that, in contrast to the critical wavelength λ c , the threshold dilatation e c is dominated by the elastic properties of the smectic LSCE. Thus - as observed in the experiments by Nishikawa et al. - e c is found to be several orders of magnitude higher than in the LMW case.