An inverse problem of diagnosing cracks using empirical mode decomposition (EMD) and Hilbert transform (HT) is proposed based on theoretically obtained vibration data of classically supported structural beam elements. The procedure to obtain natural frequencies, mode shapes and dynamic response to excitation force of pristine and damaged beams is provided. Three different damage indices are used for detecting the crack, identifying the crack height and locating the damage. It is shown that intrinsic mode functions (IMFs), instantaneous frequency time (IF) and amplitude time (A) distributions extracted from dynamically acquired response signals are able to provide information about the existence and severity of crack. This study is the first in terms of (1) employing temporal and spatial signals along with HT, (2) presenting kurtosis usage for beams with different boundary conditions and (3) deriving the deviation curves for identifying the defects in structural beam elements. The proposed procedure and damage metrics are shown to be capable of detecting cracks as small as 4-5% of beam height, and are vigorous and noise robust. © 2013 Taylor & Francis.