  In this work, we demonstrate a method for constructing the Solov'ev
equilibrium with any given 2D shape surrounded by a vacuum region using
external poloidal field coils. The computational domain consists of two parts:
the plasma region, where the solution is the same as the Solov'ev solution, and
the vacuum region, where the magnetic field generated by external coils as well
as plasma current is determined using the Green function method through a
matching condition near the separatrix. However, the method is not limited to
the Solov'ev equilibrium in particular. The accuracy, efficiency, and
robustness of such a scheme suggest that this method may be applied to the 2D
shaping of tokamak plasma with vacuum region using external coils in general.
