Unidirectional gravity-inertial spreading of oil on calm water is investigated. In this stage of spreading, gravity force is balanced by inertia force as the main resisting force. The use of Fannelop and Waldman boundary condition, based on the analogy with the acoustic limit in gas dynamics, is extended and modified to account for the case of continuous discharge of oil on water. The results yield the spreading laws and the velocity and oil-thickness profiles. The oil spill spreading results are compared with the approximate method based on the dynamics of spreading of constant-volume spill, showing that the approximate method is conservative in a certain range. (c) 2005 Elsevier Ltd. All rights reserved.