Molecular dynamics (MD) simulations based on Tersoff potential have been performed to study the mechanical properties of a β-SiC nanowire and CNT/β-SiC nanowire under tension with a constant strain rate. A tension, proportional to the deformation within Hook’s law, eventually led to a breaking of a β-SiC nanowire and CNT/SiC junction. With the diameter and axis direction of a β-SiC nanowire and simulation temperature, we calculated the curve of strain energy vs. strain. In addition, the elastic modulus of the β-SiC nanowire and a CNT/SiC junction was determined from the curve of the strain energy vs. strain. During tensile loading, the elastic modulus of the β-SiC nanowire and a CNT/SiC junction was generally decreasing with temperature and tended to increase with diameter of the nanowire. The axis of Young’s modulus (279 to 770 GPa) of the β-SiC nanowire lay along the <111> direction was considerably higher than that (110 to 200 GPa) of the β-SiC nanowire with the axis in the <001> direction. Our simulation result with the nanowire with axis of the <111> direction was in good agreement with the experimental data which was within the range from 316 to 890 GPa. In the case of a CNT/SiC junction, also we investigated the Young’s modulus. The CNT/ β-SiC nanowire (241 to 392.3 GPa) was considerably higher than that (105.2 to 299.6 GPa) of the CNT/ β-SiC junction. The  Young’s modulus was higher than that of the  orientation in a β-SiC nanowire and a CNT/β-SiC nanowire junction. We also observed that the β-SiC nanowire formed one atomic chain consisting of Si-Si bonds near the necking occurrence area; the length of the atomic chain increased with strain and eventually the nanowire fractured. This is because the bond strength of Si-Si is weaker than those of Si-C and C-C. Due to the superior mechanical properties of the CNT, tension properties in the CNT/β-SiC nanowire junction closely depended on that of β-SiC nanowire.