SiS has long been observed in the circumstellar medium of the carbon-rich star IRC+10216 CW Leo. Comprehensive and accurate rotation-vibrational line lists and partition functions are computed for 12 isotopologues of silicon sulphide ($^{28}$Si$^{32}$S, $^{28}$Si$^{34}$S, $^{29}$Si$^{32}$S, $^{28}$Si$^{33}$S, $^{30}$Si$^{32}$S, $^{29}$Si$^{34}$S, $^{30}$Si$^{34}$S, $^{28}$Si$^{36}$S, $^{29}$Si$^{33}$S, $^{29}$Si$^{36}$S, $^{30}$Si$^{33}$S, $^{30}$Si$^{36}$S) in its ground (X $^1\Sigma^+$) electronic state. The calculations employ an existing spectroscopically accurate potential energy curve (PEC) derived from experimental measurements and a newly-computed ab initio dipole moment curve (DMC). The $^{28}$Si$^{32}$S line list includes 10104 states and 91715 transitions. These line lists are available from the ExoMol website www.exomol.com and the CDS database.