The research presented in this thesis investigates new vibration-based crack detection methods in simply-supported, cantilevered and clamped-clamped beams using signal processing techniques. Different cracked beams with cracks of various depths located at different positions along the beams were simulated using the ABAQUS Finite Element Analysis (FEA) software. The difference in the modelling of cracks in this thesis compared to previous works is that the cracks in beams are modelled as hairline cracks without any widths. In previous works, cracks are mostly modelled as slots of specified widths. Initially, a comprehensive mesh study based on natural frequencies and modal displacements is performed to obtain the optimum element type and mesh structures for intact and cracked beams and the accuracy of the FEA modal data is verified using computed analytical modal data. Subsequently, the ABAQUS FEA program is used to compute the modal displacements of intact and cracked beams. From these modal displacements, the first four transverse displacement mode shapes (DMS) of the beams are extracted. Also, the natural frequencies of intact and cracked beams with stationary roving masses are computed using the ABAQUS FEA program. The natural frequencies of a beam change as an auxiliary mass, that is the roving mass, is traversed from one end of the beam to the other. This variation in natural frequencies with locations of the mass gives rise to a natural frequency curve (NFC) for the beam. From the computed natural frequencies, NFCs for the first four transverse modes of beams are derived.The simulated DMS and NFCs are used in the development of the crack detection methods which are based on the stationary wavelet transform (SWT) of the DMS and NFCs and the derivatives of the NFCs. These resulted in four distinct crack detection procedures, namely: (1) The difference of the Stationary Wavelet Transform (SWT) of two sets of augmented modal data, (2) SWT of residuals from the difference of analytical baseline data and cracked simply-supported numerical data, (3) SWT of the natural frequency curves (NFCs), and (4) derivatives of the NFCs. It is shown that the first procedure, that is the difference of the SWT detail coefficients of two sets of augmented modal data, gives high accuracy and sensitivity in detecting double symmetric and multiple cracks as well as single cracks with various depths and different locations in simply-supported, clamped-clamped and cantilevered beams. The method takes the SWT detail difference of the extrapolated odd and even data points of the original signal which increases the sensitivity of the crack detection method and also eliminates the SWT end effects. Similarly, the second procedure, which is based on the SWT of the residuals, provides accurate crack identification of single and multiple cracks. The residuals are obtained from the difference of the modal displacements of the cracked beams and the analytical intact baseline data. The application of SWT to the residuals increases the accuracy and efficiency of crack detection method. Furthermore, it is shown that the third procedure, which is the SWT of NFCs, is capable of detecting single and multiple cracks in simply-supported, clamped-clamped and cantilevered beams with high accuracy. The SWT detail coefficients of intact beams are used as a baseline data to eliminate the end effects of the SWT detail coefficients of the cracked NFCs. Finally, it is shown that the fourth procedure, which is based on the first, second and third derivatives of the NFCs of the cracked beams, is capable of detecting, locating and determining the severity of single, double symmetric and multiple cracks in beams with various boundary conditions.