The paper is concerned with damage detection in plates while using the Discrete Wavelet Transform (DWT). Rectangular plate structures resting on a Winkler or elastic half-space type foundation, with free boundaries are examined. Plate bending is described and solved by the Boundary Element Method in a direct approach. Defects are introduced by additional edges forming slots in relation to the basic plate domain. Numerical investigation is conducted basing on signal analysis of the structural static response and by taking advantage of multi-resolution analysis (MRA) of the signal function which can be represented in a multi-scale manner. The obtained signal is decomposed with the use of Daubechies or Coiflet wavelet families. The white noise generator is used to model measurement inaccuracy which is an inevitable element of a real experiment. The efficiency of DWT of the contaminated signal in damage detection is studied.