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A simplified theory of electromagnetic shielding by enclosures with conductive and/or magnetic wails is presented. The theory is based on a simplified type of boundary condition at the enclosure walls. Theoretical results are compared with exact solutions for steady-state and transient excitation and the approximation turns out to be extremely good in all cases of practical interest. For enclosures of arbitrary shapes, the problem is formulated as a single integral equation in the unknown current in the shield. Numerical solution of the equation is discussed, as well as a possible equivalent lumped-circuit representation.