One-dimensional monatomic chains are promising candidates for technical applications in the field of nanoelectronics due to their unique mechanical, electrical and optical properties. In particular, we investigate the mechanical properties including Young's modulus, ultimate strength and ultimate strain, which are necessities for the stability of the materials by the Car-Parrinello molecular dynamics in this work. The comparative studies for the alternating carbon-nitrogen (C3N2) chain and carbon chains (carbyne) of different lengths show that the carbon-nitrogen (C-N) chain is obviously stronger and stiffer than carbynes. Thus the C-N chain, which has been found in decomposition products of the nitromethane explosive simulations, could be a superior nano-mechanical material than the carbyne chain. Furthermore, it is found that the bond order of weakest bond in monatomic chains is positively correlated with Young's modulus and ultimate strength of materials.