In this report we shall discuss a method which allows to predict and to verify in an easily way numerical calculation results of the band structure of semiconducting and dielectric crystals. The method presented is based on the Zak's concept of the elementary energy bands and it is particulary useful for crystals with a large number of atoms in a unit cell. We demonstrate that the elementary energy bands create the crystal band structure, moreover, they can be obtained starting from the empty-lattice approximation completed by the general data concerning a semiconducting crystal (the existence of the forbidden gap, lattice constants, number of valence electrons in the unit cell and space symmetry group). It should be emphasized that the presented method does not require information about positions of atoms in the unit cell and gives initial information about electron density distribution and chemical bonding. Our method has been applied to the wide bandgap YAlO3 dielectric crystals, to the acoustooptic family of Tl3AsS4 crystals and, for comparison, to narrow band crystals. It was confirmed by ab initio numerical calculations of the band structure of some of these crystals. The obtained results are in a good agreement with experimental data.