We construct an idealized three-dimensional model of Saturn's magnetosphere. The total magnetospheric field is a sum of three contributions; the first two contributions are internal, in the form of a planetary dipole and an equatorial ring current deduced from Voyager observations. We concentrate on the third contribution, resulting from the interaction of the solar wind with the Kronian magnetosphere. From the balance between the solar wind ram pressure and the magnetospheric pressure, we provide simultaneously models of the magnetopause and of the magnetic field due to the surface currents on the magnetopause. The resulting magnetopause has characteristics intermediate between those of analogous Earth and Jupiter magnetospheric models. A natural day-night asymmetry arises in the total magnetospheric field. Its intensity is tested with Voyager 1 data: the third contribution improves the agreement between data and models in the outer magnetosphere. This work extends the range of a physically reliable model of Saturn's magnetosphere in latitudinal and longitudinal directions from regions where there have been observations to regions where there have not. We discuss several possible applications, particularly some relevant to the future Cassini mission. ¿ American Geophysical Union 1995