The interaction between Io and the plasma torus is simulated by a three-dimensional numerical model which allows the calculation of electric fields, current density distributions, and magnetic fields in Io's vicinity and in the Alfv¿n wings. The model is self-consistent in the sense that the influence of magnetic field disturbances on the electric field is taken into account and vice versa. A two-dimensional elliptic differential equation for the electric potential is derived by using Euler potentials. The current density in Io's vicinity is decomposed into poloidal and toroidal fields. This representation allows an effective integration to get the magnetic field disturbances. Pedersen, Hall, inertial (or polarization) and field-aligned currents are calculated. We show results for different upstream plasma conditions and atmosphere/ionosphere models and discuss the consequences of variations in neutral density, Alfv¿nic Mach number, and other parameters. A series of simple spherically symmetric atmosphere/ionosphere models with neutral gas densities between 1016 m-3 and 1017 m-3 are investigated. By comparison with Voyager magnetic field measurement we get agreement for a column density of 7.5¿1021 m-2 (surface density N0=5¿1016 m-3 , scale height H=150 km). ¿American Geophysical Union 1987