This paper deals first with the formulation of a three-dimensional numerical model intended to determine the spatial and temporal evolution of the oceanic circulation in coastal zones under the effects of various oceanic and meteorological constraints. Simulations are based on the Mobeehdycs model which was developed through collaborative work of several laboratories. Then, the paper presents the results of the application of the model to the continental shelf of French Guiana under academic but realistic climatic conditions. The application required the adaptation of the model and the use of appropriate techniques for solving the equations accounting for the peculiarities of the local constraints. The application is of importance as, because of the lack of systematic observations, the current, salinity and temperature fields at the site are poorly known. A better knowledge of these fields is recognized as of fundamental interest for a characterization of the site from the biological and the ecological viewpoints. The results clearly show the effects of the external forcing (wind and rivers) on the fields evolution, at the surface and with respect to the depth. The time scales of these evolutions as well as their mutual influence are identified. Finally, the results agree, at least qualitatively with some of the few observational results available at present.