  We extend the previous 30-band $k$$\cdot$$p$ model effectively employed for
relaxed Ge$_{1-x}$Sn$_{x}$ alloy to the case of strained Ge$_{1-x}$Sn$_{x}$
alloy. The strain-relevant parameters for the 30-band $k$$\cdot$$p$ model are
obtained by using linear interpolation between the values of single crystal of
Ge and Sn that are from literatures and optimizations. We specially investigate
the dependence of band-gap at $L$-valley and $\Gamma$-valley with different Sn
composition under uniaxial and biaxial strain along [100], [110] and [111]
directions. The good agreement between our theoretical predictions and
experimental data validates the effectiveness of our model. Our 30-band
$k$$\cdot$$p$ model and relevant input parameters successfully applied to
relaxed and strained Ge$_{1-x}$Sn$_{x}$ alloy offers a powerful tool for the
optimization of sophisticated devices made from such alloy.
