Based on the Rietveld method, the quantitative phase analysis was performed of AlMgB14-based materials obtained by self-propagating high-temperature synthesis (SHS) of Al12Mg17-B powder mixture using a chemical furnace based on titanium and silicon of various thicknesses (1, 2, and 3 cm). Al0.5Mg0.5B2, AlMgB14, MgAl2O4 phases were identified in the obtained materials: the total contribution to the integrated intensity was no less than 98%. Ab initio calculations of the lattice energy, thermodynamic characteristics, and elastic moduli of the main phases were performed both in the initial (reference) and after the refined state. The phase content in the obtained AlMgB14 materials depends on the chemical furnace thickness. In the materials obtained in the chemical furnace with a thickness of 2 and 3 cm, AlMgB14 phase is dominated, which is modified during the synthesis with an increase in the lattice stability. A sharp decrease in the elastic characteristics and specific heat of the dominant phases was found, which is expected to stimulate a change in the characteristics of the near-surface layers of the synthesized AlMgB14 materials.