[en] In this paper, we present the results of the density functional theory (DFT)- based theoretical calculations of structural, elastic and electronic properties of YMgX₄ (X = Co, Ni and Cu) compounds. For such objective, the full-potential linearized augmented plane wave (FP-LAPW) method within generalized gradient approximation (GGA-PBE) was used. Our results of structural optimization are in good agreement with other theoretical and experimental ones. Otherwise, the negative formation enthalpies of these compounds indicate their alloying ability. Our calculations also reveal that YMgX₄ are elastically stable and ductile, and their hardness increases in order: YMgCu₄ < YMgCo₄ < YMgNi₄. YMgCo₄ is a magnetic material whose magnetism is derived mainly from Co atom, while YMgNi₄ and YMgCu₄ have non-magnetic nature. Finally, the thermal properties such as heat capacities, thermal expansion, Grüneisen parameter and entropy of studied compounds were calculated using the quasi-harmonic Debye model for wide temperature range from 0 K to 1200 K, and all of them were analyzed in detail. (paper)