In the absence of the toroidal flux, two coupled quasi two-dimensional elliptic equilibrium equations have been derived to describe self-consistent three-dimensional quasi-static magnetospheric equilibria with isotropic pressure in an optimal (&psgr;,&agr;,&khgr;) flux coordinate system, where &psgr; is the magnetic flux function, &khgr; is a generalized poloidal angle, &agr;=ϕ-Δ(&psgr;,&agr;,&khgr;), ϕ is the toroidal angle, Δ(&psgr;,&agr;,&khgr;) is periodic in ϕ, and the magnetic field is represented as B=∇&psgr;¿∇&agr;. A three-dimensional magnetospheric equilibrium code, the MAG-3D code, has been developed by employing an iterative metric method. The MAG-3D code is the first self-consistent three-dimensional magnetospheric equilibrium code. The main difference between the three-dimensional and the two-dimensional axisymmetric solutions is that the field-aligned current and the toroidal magnetic field are finite for the three-dimensional case, but vanish for the two-dimensional axisymmetric case. The toroidal magnetic field gives rise to a geodesic magnetic field curvature and thus a magnetic drift parallel to the pressure gradient direction, which gives rise to the field-aligned current. ¿ American Geophysical Union 1995