Abstract The propagation into the Alboran Sea of the interface depression generated at the Strait of Gibraltar by the interaction of the semidiurnal tidal current with the main (Camarinal) sill is studied numerically by using a unidirectional model with two horizontal space dimensions. An initial waveform within the strait is determined whose evolution corresponds with the train of internal solitary waves detected in the Alboran Sea by means of current measurements at different depths, as described by Kinder. The agreement is good for two points located at about 45 km east of the strait, the first aligned with the strait axis and the second 20 km to the north. Moreover, the shape and amplitude of this initial condition are in agreement with a typical interface depression generated in the strait by the interaction of the tidal current with the sill. A series of numerical experiments with different initial conditions is also performed to study the sensitivity of the model results to changes in the initial i...