The finite element variational formulation of the impedance boundary condition (IBC) is applied to solve two-dimensional eddy current problems, especially at high frequencies in electrical machines. This formulation is used to compute the ac resistance and the self inductance per unit length of both a reverse ‘T’ slot-embedded conductors and a simple slot-embedded conductor. The proposed IBC formulation is very efficient, because it does not change the sparsity of the finite element global matrix as well as it has minimized the computing cost such as computer memory and central processing unit time. The obtained results of both the finite element method (FEM) and the IBC formulation are compared with published results.