The so-called brick layer model is frequently used to analyze impedance spectra of polycrystalline samples with highly resistive grain boundaries. However, the basic assumptions of the model (cubic grains, laterally homogeneous grain boundaries, identical properties of all grain boundaries) are usually violated in real ceramics. To investigate the impact of some deviations from the brick layer model, the potential distributions, and thus the impedance of polycrystals, have been calculated by the finite element method. The results show that bulk properties can distinctly influence the size and shape of the so-called 'grain boundary semicircle', particularly for laterally inhomogeneous grain boundaries and for properties varying from boundary to boundary. Depressions of the grain boundary semicircle solely due to a non-brick-layer microstructure are observed. The validity and limits of the brick layer model are discussed.