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The magnetic shielding effect of superconducting plates is investigated by means of the numerical simulation. Shielding plates are assumed to have a multiple-layer structure and each layer is assumed to be thin enough. As the critical state model of the superconductor, a modified Bean model is adopted so that the current density may not exceed the critical one. Under these assumptions, the governing equation of the shielding current is expressed in terms of the normal component of the current vector potential. A two-dimensional numerical code to integrate the equation has been developed and the time evolution of the shielding currents is followed by use of the code. The results of computations show that the shielding currents concentrate extremely in the vicinity of the boundary. This is mainly because the effective conductivity of the superconductor becomes sufficiently large that the problem constitutes a singular perturbation problem. In addition, It turns out that the shielding coefficients depend on neither time nor frequency of the imposed magnetic fields.