An integral-equation approach has been used to solve eddy current problems. The conducting material is represented by a network of current-carrying line elements. Consequently, Maxwell's field equations can be replaced by Kirchhoff's circuit rules. The loop equations for voltages, supplemented by the node equations for the currents, comprise a set of linear equations that can be solved repeatedly to give the time development of the eddy currents. Currents, magnetic fields, and power are calculated at each step. For a two-dimensional geometry, either thin plates or infinite cylinders can be calculated. Rectangular and circular cross sections have been calculated with good agreement to analytical expressions. Thin curved shells have also been calculated.