Based on first-principles calculations and theoretical analysis, we investigated various properties of pristine monolayer M2C (M = V, Nb, Ta). Firstly, we optimized the structures of monolayer M2C and computed the corresponding electronic band structures, the results show that they are metallic. And there exists Dirac points in the band structure, which make them may being potential candidates for investigating Dirac-physics-based applications. Secondly, we analyzed the phonon spectra combining with the corresponding projected phonon density of states of monolayer M2C. The results indicate that the three monolayers M2C are dynamically stable. The large energy gap between the optical phonon ZO and ZO' mode gets wider with the mass of translation metal increasing. Thirdly, the related thermodynamic properties, such as the Raman (E g, A 1g), infrared active (E u, A 2u) mode, Debye temperature, sound speed, temperature-dependent heat capacity, entropy, free energy and lattice thermal conductivity were also investigated. Finally, the planar elastic stiffness coefficients and other derived elastic properties of monolayer M2C were determined. We find that the Y s value of Nb2C and Ta2C is larger than that of monolayer Ti2C (130 N m-1). By using the uniaxial tensile, we obtained the stress-strain properties of monolayer M2C. The monolayer Ta2C has the strongest peak strength in the direction of armchair. Its maximum stress is 83GP at ε arm = 0.19. Thus, those MXene materials can be considered as extremely stiff 2D materials.