The mechanical behaviors of carbon nanocone (CNCs) with equivalent number of atoms under uniaxial extension and uniaxial compress are investigated using classical molecular dynamics simulations, exploring the Brenner and Lennard-Jones potentials to represent the interatomic interaction. The mechanical properties including elastic strain limit, ultimate longitudinal loading, and configuration evolution of CNC, are obtained and compared with those of carbon nanotube that consists of equivalent atoms. Under tension, CNC with larger apex angle presents a higher failure strength in general, as well as a larger maximum strain. However, the failure strength of the CNC with largest conical angle of 112.88° is the smallest one. The carbon nanotube with (15, 0) and 4 nm length presents a moderate strength and strain. Under compression, CNCs with conical angle of 112.88° and 83.62° have true chiral inversion without the chemical bond break. However, the other CNC exhibits unstable uniaxial compress and sudden lateral bend under compression. The force that buckles these carbon nanostructures decreases as the conical angle increases, except for the CNC of 38.94°. Results in the present study show that a certain CNC possesses more excellent mechanical properties than the equivalent CNT and is expected to substitute CNT and to be applied to some engineering fields such as nanosensors and nanoscale composites.