We investigate the structural, elastic, electronic and magnetic properties of the Heusler compounds Cu 2 MnSi, Cu 2 MnAl and Cu 2 MnSi 1−x Al x quaternary alloys, using the full-potential linear-augmented plane-wave method (FP-LAPW) in the framework of the density functional theory (DFT) using the generalized gradient approximation of Perdew-Burke-Ernzerhof (GGA-PBE). Our results provide predictions for the quaternary alloy Cu2MnSi1−xAlx (x = 0.125, 0.25, 0.375, 0.5) in which no experimental or theoretical data are currently available. We calculate the ground state's properties of Cu2MnSi1−xAlx alloys for both nonmagnetic and ferromagnetic configurations, which lead to ferromagnetic and metallic compounds. Also, the calculations of the elastic constants and the elastic moduli parameters show that these quaternary Heusler alloys are ductile and anisotropic.