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A new nondestructive method of assessing brick wall dampness by means of a model electrical impedance tomography constructed for this purpose was described. The assessment is based on the distribution of conductivity inside the tested wall, determined from numerically processed surface potential measurement results. The system includes: measuring probes, an excitation signal generator with power amplification, a multichannel selector-multiplexer with galvanic separation, and a computer set. The proposed method was verified by simulations and its main components were verified experimentally in laboratory conditions. The conductivity distributions determined by the impedance tomography method were compared with the results obtained by the conventional dry-weight method. Satisfactory agreement between the results was found. Further research aimed at implementing this nondestructive method in building engineering practice is underway.