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A theory is presented here to obtain the electromagnetic field in a multiregion cylindrical induction device with arbitrary two‐dimensional current sheet excitation. This theory is based on the transfer‐matrix method and provides a closed‐form solution. It applies also to the case of one‐dimensional excitation where it reduces to the known results presented by Freeman [Freeman, IEE Proc. 121, 1117 (1974); Greig and Freemen, IEE Proc. 114, 1681 (1967); Freeman and Blank, IEE Proc. 123, 149 (1976)]. A numerical example is shown, and it is in good agreement with published data.