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A theoretical study of polarization-spectral anomalies of wave fields, or their deviations from the predictions based on simple plane-wave models, is presented. A simple unified method of numerical simulation of anomalies of nonstationary wave fields near a caustic and in the penumbra is described. It uses both the leading and correcting terms in asymptotic expansions. Examples of calculation of displacements and average polarization ellipses are given. Qualitative properties of wave fields are discussed. A review of earlier research on polarization anomalies of elastic waves is given. Bibliography:38titles. [ABSTRACT FROM AUTHOR]