Abstract: The first-principles calculations were performed on a series of quaternary Heusler compounds using the all-electron full-potential linearized augmented plane wave (FLAPW) method. The computed elastic constants revealed that 28 compounds exhibit mechanical stability. Calculations and mechanical property analysis of the Young's modulus, shear modulus, Poisson's ratio, and shear anisotropy for each compound showed that all mechanically stable compounds possess shear anisotropy. Magnetic moment analysis identified 12 compounds satisfying the Slater-Pauling rule. Further band structure and density of states analyses for these 12 compounds demonstrated excellent semimetallic characteristics. These findings provide crucial theoretical support for the application of quaternary Heusler compounds in the fields of materials science and electronics.