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The paper proposes an iterative procedure, called current iteration, for the finite element solution of two-dimensional steady-state skin effect problems in open boundaries. In the procedure a fictitious boundary is introduced enclosing all the conductors. On it, the magnetic vector potential is first guessed and then iteratively updated according to the current density computed in the conductors. Conditions are obtained implying convergence to the exact solution of the unbounded problem whatever the initial guess. The choice of the fictitious boundary and the selection of the relaxation parameter in such a way that computational efficiency is obtained are discussed. The greatest advantage of the procedure is its ease of implementation in a pre-existing finite clement code for bounded problems. An axisymmetric version of the procedure is also described since implementation only involves minor changes as compared with the 2-D one. Examples are provided in order to clarify and validate the procedure and compare it with other techniques. [ABSTRACT FROM AUTHOR]