Recently, two dimensional silicon carbide (2D-SiC) is expected to be a promising semiconductor for nanoelectronics and nanoelectromechanical systems (NEMS) due its exceptional electronic, thermal and mechanical properties. Although numerous studies have been performed on the characterization of structural and electronic properties of 2D-SiC, the thermal and mechanical behaviors have not been well studied. In this dissertation, non-equilibrium molecular dynamics simulation has been performed to explore the thermal properties of 2D-SiC. Moreover, the mechanical behaviors of 20-SiC are quantified using the virial stress based molecular dynamics simulation. This dissertation provides many new important findings based on these simulations such as a slowly decreasing trend of thermal conductivity in the high temperature region, deviating the -1/T law due to the influence of high frequency pbonons and Umklapp limited phonon scattering. The simulated thermal conductivity of 2D-SiC using optimized tersoff potential is found as -271.03 W/mK at a length of 600 run which is one order higher than silicene of the same length. However, due to the lower acoustic group velocities, lower Debye temperature, and additional phonon scattering effect of the binary SiC system, the reported thermal conductivity is much lower than graphene. The phonon density of states (PDOS) shows a strengthening behavior of the low frequency acoustic peaks with the increase of sheet length, quantifies the increasing trend of thermal conductivity with length at room temperature. Above room temperature a shrinking trend of acoustic phonon peaks is noticed, conveys the causes of decreasing trend of thermal conductivity with temperature. However, due to the consideration of ground state phonon modes in specific heat capacity, the quantum corrected thermal conductivity shows an increasing trend up to Debye limit. In addition, it is found that the optimized tersoff potential provides a better estimation of the thermal conductivity than the original tersoff potential due to proper parameterization of the SiC system with analytical model. Further, the mechanical behaviors of pristine and defected 2D-SiC have been studied. The effect of point, bi, and mixed vacancy defects on the tensile strength and elastic modulus have been determined. The estimated tensile strength and elastic modulus of pristine 2D-SiC show a linear reduction trend with temperature due to the strong thermal variation effect. For pristine 20-SiC, a tensile strength of 53.625±7 GPa with a failure strain of 0.153 is found at room temperature. However, with the introduction of vacancy defects, the tensile strength and elastic modulus of 20-SiC reduces significantly due to the symmetry breakdown and the bond breaking effect. Among the three types of vacancy, the point vacancy shows the most treacherous effect on the tensile strength and elastic modulus due its greater bond breaking effect. It is found that for 1 %-point vacancy, the tensile strength is reduced about 66.35% from that of pristine case. Therefore, these findings are very much important to understand new phonon transport physics and potentially lead to not only in nanoelectronics and nanoelectromechanical systems, but also in novel applications of 2D-SiC in various emerging fields.