This thesis develops an analytical model to predict the cross-correlation functions of leak signals in plastic pipes. The model explains some of the acoustic characteristics of the measured leak signal in plastic water pipes. Moreover, it is used to study the effects of the cut-off frequencies of high and low-pass digital filters used to remove noise, and the selection of acoustic/vibration sensors on the correlation technique. The importance of the cut-off frequency of the high-pass filter and the insensitivity of the correlation to the cut-off frequency of the low-pass filter are demonstrated using the model. A criterion for selection of acoustic/vibration sensors using frequency information is defined. Theoretical predictions show that a measure of pressure responses using hydrophones is effective for a small signal to noise ratio (SNR). Otherwise, a relatively definite peak correlation can be achieved using leak signals measured by accelerometers. To locate the position of a leak, accurate estimation of the time delay between two measured signals plays a dominant role. Coupled with the model for wave propagation along plastic pipes, various time delay estimators using cross-correlation are compared for their ability to locate a leak in plastic pipes. For leak detection in plastic water pipes it is found that the prewhitening processors, particularly the smoothed coherence transform (SCOT) estimator is well suited to this purpose. Theoretical analysis shows that random errors introduced by random noise on the signal measurements are insignificant compared with the resolution of the time delay estimators imposed by the low-pass filtering characteristics of the pipe. Based on the phase spectrum between two sensor signals, a coherence weighted phase spectrum (CWPS) method implemented in the frequency domain is proposed for time delay estimation. It suppresses those frequency regions where there is poor coherence between the signals so as to improve the accuracy of the time delay estimator. Compared to the correlation technique, it turns out to be fully consistent with the phase transform (PHAT) and SCOT methods. Experimental work including some tests in actual water pipes and MDPE pipe in-vacuo is carried out to validate their accuracy and effectiveness.