ABSTRACT One of the most important Si-bearing species in the intersellar medium is the SiS molecule. Thermal rate coefficients and other collisional properties are calculated for its formation via the title reaction using the quasi-classical trajectory method. An accurate representation of the HSiS potential energy surface is employed, which has been modelled from high-level ab initio calculations and a reliable description of long-range interactions as implied by the underlying double many-body expansion method. The calculated rate coefficients for the $\rm SiH + S → SiS + H$ reaction can be modelled with k(T) = α(T/300)βe−γ/T where $α =0.63\times 10^{-10}\, \rm cm^3\, s^{-1}$, β = -0.11, and $γ = 11.6\, \rm K$. This result is only slightly lower than that for SiS formation via Si + SH collisions. The contribution of each reaction mechanism and the rovibrational energy distributions of the nascent SiS molecule are also calculated. The title collision can also yield SH ($\rm SiH + S → SH + Si$), but the corresponding rate coefficient is 20 to 27 times smaller than for SiS formation ($α =0.025\times 10^{-10}\rm cm^3\, s^{-1}$, β =-0.13, and $γ = 9.38\, \rm K$). The role of intersections between excited electronic states is also discussed, based on novel calculations including eight electronic states.