Abstarct: This thesis has proposed a model-baxsed leak detection method along finite length pipelines. First of all momentum and continuity equations, have been used to model the pipeline in form of parabolic partial differential equations which describe system dynamics. In order to solve and discretize these equations, the method of characteristics has been used. The next step was describing the pipeline system in state space form. Two fictitious leaks were defined at known locations. These two leaks have been considered as states of the system. Then proper input and output parameters have been considered and system states have been estimated by Extende and Cubature Kalman filters. OLGA simulator was introduced in the last chapter to simulate the proposed method. Convergence of system states and comparison of leakage estimation error, confirmed the proposed method efficiency.