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Numerically optimized specific absorption rate (SAR) distributions in a source-free three-dimensional multilayered concentric cylindrical (MCC) model are presented. The fields were expanded in the modes of the MCC. Cost functions which mathematically specify the relative weight assigned to differences between an SAR distribution and a desired SAR distribution were defined. The coefficients of the modes, which minimize the cost function, were obtained using gradient search optimization methods. The optimized SAR distributions shown were computed using three cost functions and two radial locations for the center of the region where the desired SAR is largest. A five-layered model, including the outer water layer for cooling and improved matching with the source, was used. The frequency was 70 MHz. The current and charge distributions computed on a perfectly conducting cylindrical surface just outside the model are given. The surface current and charge distributions depends strongly on the relative importance of the cost for acute heat and systemic heat. A technique is developed for generating a new set of basis functions for reducing the number of unknowns to be optimized.