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The magnetic field was applied for identification of a shape of an inaccessible boundary between substances of different magnetic properties. Taking advantage of the conception of substitute field sources a mathematical model of the problem was described by means of the potential theory and integral equations. Numerical processing of Fredholm integral equations of the first kind appearing in the above model leads to a system of ill‐posed and non‐linear algebraic equations. This results in numerical instability. The problem was solved by the use of the fixed‐point technique based on Brouwer’s theorem. A few numerical examples were illustrated for the selected shape of the investigated boundary.