A method of choosing a smoothing parameter is described and illustrated for the problem of a photo-elastic analysis of the bending vibrations of a plate. The finite-element model of the system is based on an approximation of the nodal displacements, while the formation of fringes is governed by the stress field in the photo-elastic coating. Without smoothing the reconstructed patterns of the fringes exhibit a non-physical behaviour at inter-element boundaries. When the smoothing parameter is too big, an over-smoothed image isobtained, which may look acceptable but be far from the realistic photo-elastic image. The presented strategy for the selection of the optimum smoothing parameter is generalised for two-dimensional Lagrange finite elements.