In this article, the structural, elastic, electronic, and magnetic characteristics of both regular and inverse Heusler alloys, Sc2TiAl and Sc2TiSi, were investigated using a full-potential, linearized augmented plane-wave (FP-LAPW) method, within the density functional theory. The optimized structural parameters were determined from the minimization of the total energy versus the volume of the unit cell. The band structure and DOS calculations were performed within the generalized gradient approximation (GGA) and modified Becke–Johnson approaches (mBJ-GGA), employed in the Wien2K code. The density of states (DOS) and band structure (BS) indicate the metallic nature of the regular structure of the two compounds. The total spin magnetic moments for the two compounds were consistent with the previous theoretical results. We calculated the elastic properties: bulk moduli, B, Poisson’s ratio, ν, shear modulus, S, Young’s modulus (Y), and the B/s ratio. Additionally, we used Blackman’s diagram and Every’s diagram to compare the elastic properties of the studied compounds, whereas Pugh’s and Poisson’s ratios were used in the analysis of the relationship between interatomic bonding type and physical properties. Mechanically, we found that the regular and inverse full-Heusler compounds Sc2TiAl and Sc2TiSi were stable. The results agree with previous studies, providing a road map for possible uses in electronic devices.