We have generated an ab initio three-dimensional potential energy surface (PES) for the (A(1)) over tildeA' state of LiSH. The spectroscopic data calculated from a full quartic force field are in very good agreement with the values obtained from microwave spectroscopic experiments. The PES has been used to solve variationally the nuclear motion problem and the vibrational energy levels are given up to about 3500 cm(-1) for LiSH and 2400 cm(-1) for LiSD. For LiSH, the anharmonic fundamental modes lie at 2571 (SH stretch), 578 (LiS stretch) and 372 (LiSH bending), and for LiSD the corresponding values are: 1866, 582 and 276 (all values are in cm(-1)), respectively. Anharmonic resonances between the bending and the LiS stretching modes are identified in both species. The calculated electric dipole moment mu(e) = 7.03 debye mirrors the strong charge separation in the lithium hydrosulphide. The electronically excited states up to vertical transition energies of 36 000 cm(-1) predissociate along the Li...SH path.