Two-dimensional (2D) transition metal carbides and nitrides, known as MXenes, have gained notable attention recently because these super-strong materials have many promising applications. In this study, computational analysis is conducted to explore the in-plane elastic constants, 2D stiffness and shear modulus of oxygen terminated M4X3 MXenes by means of the density functional theory (DFT) calculations. Our results reveal that the binding site of the oxygen atoms can greatly affect the mechanical properties. The crystal orbital Hamilton population (COHP) analysis suggests that the impact of the oxygen-binding site is because the M − O bonding strength can significantly influence their mechanical stiffness. Our outcomes may, therefore, provide the theoretical foundation for the advance of MXene-based applications in mechanical engineering.