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A symmetric coupling of methods of finite and boundary elements for numerical solution of transient eddy current problems is described. This is an essential step in modelling of electromagnetic forming of metalic sheets. The finite element method is employed in the conducting region of the metalic sheet. The boundary element method relies on the Stratton-Chu representation formula and it models the electromagnetic field in the air including its decay at infinity. We impose external currents by the Biot-Savart law.