Structural health monitoring systems have a great potential for cost saving and safety improvement in different types of structures. One of the most important tasks of these systems is to identify damage at an early stage of its development. A variety of methods may be used to identify, locate, or quantify the extent of damage or fault in a structural or mechanical component. However, the preferable method is the one which maximises the probability of detecting the flaw, while also considering feasibility of in-situ testing, ease of use and economic factors.Cracks are one of the common defects in structural components that may ultimately lead to failure of structures if not detected. The presence of cracks in a structure brings about local variations in the stiffness of the structure. These variations cause the dynamic behaviour of the cracked structure to be different from that of a healthy one. Vibration-based damage detection methods have attracted considerable attention over the past few decades. These methods generally use changes to the physical properties of structures for the purpose of crack detection. In this thesis, two new vibration-based methods have been developed for damage detection in beam-like and rotor-type structures. The first method performs the entire signal processing required for crack detection in time domain. It is based on assessing the normality of vibration responses using the normal probability plot (NPP). The amount of deviation between the actual and normal distribution of measured vibration responses was calculated along the length of the structure to localise the crack.The second proposed method converts the vibration responses into frequency domain for further processing. Excitation of the cracked structure at a given frequency always generates higher harmonic components of the exciting frequency due to the breathing of the crack. This method uses the operational deflection shape of the structure at the exciting frequency and its higher harmonics to identify the crack location.Avoiding complicated signal processing in frequency domain is the main advantage of the first method. However, more precise identification of crack locations can be obtained through the second method. Generally, both methods have the advantage of being easy, reference-free and applicable to in-situ testing for any structure. The concept and computational approach of both methods along with their validations through numerical and experimental examples have been presented. Moreover, different input excitations have been used to evaluate the capability of the developed methods in detecting the crack location(s).