Leaks in pipelines contribute to the environmental pollution, promote corrosion and equipment failures and produce instabilities in the pipeline operation and control. Leaks are inevitable as third party damage, equipment failures, and errors in pipeline design and operation do occur. Being able to accurately detect the location of leaks is imperative. One objective of this paper is to develop a mathematical model that accounts for the behavior of pressure and flow-rate profiles in leaky pipeline systems. Such a mathematical model is needed to better understand the dynamic behavior of the pipeline and its characteristics and for the detection the leak locations. The paper also involves computer simulation of pipeline conditions using the developed mathematical model and Kalman filtering technique. Leak localization is accomplished by a marching scheme that scans the pipeline from the inlet side to the outlet side to find the location at which the minimum residuals are obtained. Simulation results are reported to demonstrate the effectiveness of the proposed leak localization scheme.