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This paper presents an analytical method for approximating the eddy current and hysteresis losses in a system of multiple sheathed cables placed in any configuration inside a steel pipe. The method is based on the theory of images, which this paper expands to apply to pipes having high magnetic permeability and high electric conductivity at the same time. The method of images, in combination with approximating the cable conductors and sheaths as multiple physical filaments, is used to compute the final current distributions in the cables and pipe and, thus, the associated losses. The accuracy of the proposed method is assessed against numerical solutions obtained using the Maxwell finite-element program by Ansoft.