The unintentional release of fluid from pipelines is considered as a leak. Leaks contribute to the environmental pollution, promote corrosion and equipment failures and produce instabilities in the pipeline operation and control. There is a need, therefore, to develop an effective leak diagnosis scheme in pipeline systems that can detect the occurrence of any leak in the system. One objective of this paper is to develop a mathematical model that accounts for the behavior of pressure and flow-rate profiles in pipeline systems with multi leaks. Such a mathematical model is needed to better understand the dynamic behavior of the pipeline and its characteristics and for the detection the leaks. The paper also involves computer simulation of pipeline conditions using the developed mathematical model. A leak detection scheme is developed that is based on a computational pipeline monitoring method. This method evaluates the mismatch between the actual variables and those of the healthy pipeline system. The pipeline conditions during normal operation were simulated and the system state variables were computed in real time based on simulated measurements collected at few selected locations along the pipeline. The underlying pipeline variables are estimated by applying Kalman filtering technique.