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This paper describes and discusses the use of the boundary element method to reconstruct the induced current density and specific absorption rate (SAR) distribution within a phantom of arbitrary shape, starting from field values on its external surface. The accuracy of the proposed approach is evaluated by comparison with the results given by other techniques in the solution of the whole electromagnetic problem, including also the sources. The influence of the parameters which could affect the reconstruction accuracy is deepened. The encouraging results obtained can open the way to a noninvasive experimental-computational procedure for the SAR evaluation.