Calculations of electron energy near edge structures (ELNES) are compared with experimental data obtained in a high-resolution transmission electron microscope. This study concerns small precipitates of aluminium nitride in low carbon steel. The ELNES technique allows to clearly establish that these precipitates crystallize in a cubic rather than in a hexagonal crystallographic cell. The influence on simulated spectra of different parameters are investigated: the size of the atomic shell and its relation with the electron inelastic mean free path. We also examine the influence of the core hole and the sensitivity to cell parameters. We particularly examine the Al L(23) near edge structure and features relating to the different transition channels (A(1g), E(g) and T(2g)). Results of a multiple scattering and band structure calculations using ICXANES and WIEN97 codes, respectively, are compared in the region from 0 to 30 eV above the edge onsets. Both calculations are in a rather good agreement.