The strength, hardness, and lattice vibrations of two superhard carbon allotropies, Z-carbon and W-carbon are investigated by first-principles calculations. Phonon dispersion calculations indicate that Z-carbon and W-carbon are dynamically stable at least up to 300 GPa. The strength calculations reveal that the failure mode in Z-carbon is dominated by the tensile type, and the  direction is the weakest one. In W-carbon, the failure mode is dominated by the shear type, and the (101)[111̄] direction is the weakest one. Although the ideal strength of diamond is distinctly greater than that of Z-carbon and W-carbon, the tensile strength and shear strength for Z-carbon and W-carbon show much lower anisotropies than that of diamond. The hardness calculations indicate that the average hardness of Z-carbon is less than that of diamond but greater than that of the W-carbon, M-carbon, and body-centered-tetragonal-C 4 carbon. The simulated Raman spectra show that the A g modes at 1094 cm -1 for Z-carbon and 1109.7 cm -1 for W-carbon are in agreement with that of 1082 cm -1 observed in the experiment of cold-compressed graphite at 9.8 GPa.