SiH has long been observed in the spectrum of our Sun and other cool stars. Computed line lists for the main isotopologues of silicon monohydride, 28 SiH, 29 SiH, 30 SiH and 28 SiD are presented. These line lists consider rotation-vibration transitions within the ground X 2 Π electronic state as well as transitions to the low-lying A 2 ∆ and a 4 Σ − states. Ab initio potential energy (PECs) and dipole moment curves (DMCs) along with spin-orbit and electronic-angular-momentum couplings between them are calculated using the MRCI level of theory with the MOLPRO package. The PEC for the ground X 2 Π state is refined to available experimental data with a typical accuracy of around 0.01 cm −1 or better. The 28 SiH line list includes 11,785 rovibronic states and 1,724,841 transitions with associated Einstein-A coefficients for angular momentum J up to 82.5 and covering wavenumbers up to 31340 cm −1 (λ < 0.319 µm). Spectra are simulated using the new line list and comparisons made with various experimental spectra. These line lists are applicable up to temperatures of 5000 K, making them relevant to astrophysical objects such as exoplanetary atmospheres and cool stars and opening up the possibility of detection in the interstellar medium. These line lists are available at the ExoMol (www.exomol.com) and CDS database websites.