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The article defines and explains methods for detecting and locating damage and quantifying its extent on an example of a finite element model of a simple beam. The defined methods are based on a comparison of the decreases in the bending natural frequencies of the nominally damaged models against the intact model. This comparison assigns natural frequency decreases to curvature of a specific mode shape, which allows creation of an analytical reference model using polynomial regression, which assigns relative natural frequency decreases to the position on the beam. The localisation method assumes that the vector of the relative natural frequency decrease ratios are unique for each position on the beam. The quantification method considers as a relevant comparative quantity, slopes of relative natural frequency decreases, as a function of damage extent. Examples of damage localisation and quantification are defined, and the relative errors of these methods are analysed.