The mechanical and thermodynamic properties of four ytterbium carbides with increasing carbon content have been examined using ab initio calculations based on density functional theory. In order to describe the strong on-site Coulomb repulsion among localized 4f electrons, generalized gradient approximation plus a Hubbard parameter (GGA + U) formalisms have been adopted for the exchange correlation term. The elastic constants of YbC, Yb2C3, YbC2, and YbC6 are related to Hubbard U. The bulk modulus B, shear modulus G, and Young's modulus E are evaluated through Voigt-Reuss-Hill approximation. Among the four ytterbium carbides, YbC6 yields the largest B, G, and E, and YbC2 exhibits relatively soft and ductile characteristics. Mechanical anisotropy was estimated using several anisotropic indexes and factors. The anisotropic property of E of four ytterbium carbides is more evident than that of B. A phonon calculation reveals the thermodynamic stability of YbC2 and YbC6, which is consistent with experimental observations.