The authors describe the application of a three-dimensional eddy current formulation to the problem of the calculation of the current density distribution in the bars of cage rotor induction machines with radially ducted rotors under steady-state conditions. The most suitable choice of formulation and its application to the ducted rotor problem are considered, and the rotor model and boundary conditions are described. Results are given in terms of the variation of the current density distribution and power loss along the bar, illustrating the effect of the ducts on the bar resistance. >