The inverse problem of decomposing uncontrolled water flow to the unregistered consumption and the leakage in mains and water distribution networks is considered. A mathematical model is proposed for the determination of unregistered consumption and leakage using the heads and flows at the inlet and at the outlet of the main or at some nodes of the network. The cases of discretely and continuously distributed water consumption in mains are thoroughly analysed and equations for the determination of respective parameters derived.