  We study the electronic and optical properties of strained single-layer SnC
in the density functional theory (DFT) and tight-binding models. We extract the
hopping parameters tight-binding Hamiltonian for monolayer SnC by considering
the DFT results as a reference point. We also examine the phonon spectra in the
scheme of DFT, and analyze the bonding character by using Mulliken bond
population. Moreover, we show that the band gap modulation and transition from
indirect to direct band gap in the compressive strained SnC. The applied
tensile strain reduces the band gap and eventually the semiconductor to
semimetal transition occurs for 7.5\% of tensile strain. In the framework of
tight-binding model, the effect of spin-orbit coupling on energy spectrum are
also discussed. We indicate that while tensile strain closes the band gap,
spin-orbit gap is still present which is order of $\sim 40$ meV at the $\Gamma$
point. The substrate effect is modeled through a staggered sub-lattice
potential in the tight-binding approximation. The optical properties of
pristine and strained SnC are also examined in the DFT scheme. We present the
modulation of real and imaginary parts of dielectric function under applied
strain.
