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The problem of low-frequency shielding of a loop axially perpendicular to a plane shield of infinite extent is analyzed by 1) the thin shield work of S. Levy, 2) solution of the vector wave equation, and 3) application of the transmission theory of shielding of Schelkunoff. Experimental data are obtained and compared with results of parts 1) and 3) in the frequency range 100 Hz to 50 kHz. The first analytical technique is not general, and the limits of applicability of the results are discussed. In the second solution, which is general, expressions are derived for the total electric and magnetic fields on both sides of and within the shield. The resulting expression for shielding effectiveness is not solved because of its complexity. The results of the third theory are adapted to the problem. The shielding effectiveness expression S = R + A + B is computer evaluated for the six shields considered (1/16-inch and 1/8-inch thick aluminum, copper, and steel). Although some approximations are made, this analytical method is the most useful in predicting the insertion loss of the shield, since the theory includes those parameters neglected in the first analytical technique.