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The structural, electronic and elastic properties of full- Heusler alloys Co2CrZ (Z=Si,Al) and their quaternary compound Co2CrSi1-xAlx, are determined using the full potential linearized augmented plane waves (FP- LAPW) method based on (GGA) the Generalized Gradient Approximation and density functional theory (DFT) implemented in the WIEN2k package. As results, quaternary compound in CuHg2Ti-type crystal structure are stable. Density of states (DOS) and bands structure show the existence of energies band gaps in their minority-spin channels with half-metallic behavior. The lattice constant of new quaternary alloys Co2CrSi1-xAlx exhibits a small deviation from Vegard's law and a marginal deviation of the bulk modulus from linear concentration. The three independent elastic constants (C11, C12, and C44) are calculated from the direct computation of the stresses generated by small strains. Besides, we report the variation of the elastic constants as a function of pressure as well. From the calculated elastic constants, the mechanical character of Co2CrSi1-xAlx is predicted; elastic constants are calculated to investigate stability criteria and the mechanical nature of the studied materials. The quaternary compound is found to be mechanically anisotropic, ductile and meet the elastic stability criteria. A regular solution model is used to investigate the thermodynamic stability of the alloy which essentially shows a miscibility gap phase by calculating the critical temperatures of the alloys.