Stratified structures have a widely usage in aerospace technologies. Free oscillation testing method (FOM) used for testing of stratified structures with large acoustic decay coefficient. Early faults detection was performed by analysis of energy spectrum of recorded mechanical oscillations, But sizes and depths of faults can not be estimated using this method. For the first time estimation of fault's size and depth performed by us using two new ideas: 1. transient (non spectral) characteristics in FOM was measured and considered as a non stationary signals; 2. wavelet packet algorithm used for analysis of such signals. We have found signal basis in Pollen parameter space for analyzing FOM signal using modification of wavelet packet algorithm. Discriminant function (DF) associated with faults' size is linear. DF associated with faults' depth is one-valued. This method also can be useful for tasks of mine and mine-like targets detection.