In this paper, a mathematical model for ship squat in highly restricted waterways is proposed. This model, which is based on the extension of Schijf's (1949) theory to dynamic effects, indicates stable and unstable squat positions for a ship. Furthermore, the transition effects are integrated into this model to simulate the behaviour of a vessel during and after an acceleration phase. This model shows that, although the vessel speed is lower than the Schijf limiting speed, grounding due to the oscillations generated at the end of the acceleration phase may occur when the unstable equilibrium position is reached. The results given by the mathematical model are validated by a numerical model based on finite element analysis.