Istanbul Strait is the only waterway connecting the Black Sea to the Mediterranean. It is subject to an ever increasing traffic with the number of vessels crossing it of the order of 50 000 in year 2001. The sinuous shape of the strait, its narrowness and shallowness make it a very challenging seaway, especially for large tankers. In the past there have been several accidents with resulting oil contaminations at the Black Sea and Marmara Sea mouths of the strait. We fear a similar accident in the middle section of the strait, both sides of which are inhabited by a population of several millions and crossed by only two suspended bridges. In this paper, we present a numerical model of the contaminant spread in the Istanbul Strait after a tanker accident. We assume that for the purposes of our study Shallow Water Equations (SWE) represent the flow field adequately. Based on this set of partial differentials equations we choose to compute the flow field by finite elements method, certainly the most appropriate spatial discretisation technique for the complicated geometry of the strait. The solution of the resulting set of nonlinear ordinary differential equations in time variable is carried out either by implicit or explicit methods. The simulation of the contaminant transport phenomenon is achieved by the finite element solution of the transport equation on the same mesh. Maps depicting the contaminated areas are displayed for different time periods after the occurrence of the oil spill accident. These results show that oil dissemination along the Bosphorus strait is a rather quick phenomenon, which takes place in a few hours. This dissemination speed does not leave much time to react and to mitigate the hazard. One must remember that 10 million people inhabit the two shores of the strait, linked by two bridges, on the one hand, and that the city of Istanbul is the major economical center of Turkey contributing to GNP by 50% on the other hand. For these reasons, the drastic consequences of an oil tanker accident can easily be understood. This pinpoints the urgency to pay attention to rescue efforts and, above all, the important precautions to take in order to avoid any kind of accident all along the 32 km long strait.