The rotation-torsion energies in the electronic ground state of HSOH are obtained in variational calculations based on a newly computed ab initio CCSD(T)/aug-cc-pV(Q+d)Z potential energy surface. Using the concept of the reaction path Hamiltonian, as implemented in the program TROVE (theoretical rovibrational energies), the rotation-vibration Hamiltonian is expanded around geometries on the torsional minimum energy path of HSOH. The calculated values of the torsional splittings are in excellent agreement with experiment; the root-mean-square (rms) deviation is 0.0002 cm(-1) for all experimentally derived splittings (with J < or = 40 and K(a) < or = 4). The model provides reliable predictions for splittings not yet observed. The available experimentally derived torsion-rotation term values (with J < or = 40 and K(a) < or = 4) are reproduced ab initio with an rms deviation of 1.2 cm(-1) (0.7 cm(-1) for J < or = 20), which is improved to 1.0 cm(-1) (0.07 cm(-1) for J < or = 20) in an empirical adjustment of the bond lengths at the planar trans configuration. The theoretical torsional splittings of HSOH are analyzed in terms of an existing semiempirical model for the rotation-torsion motion. The analysis explains the irregular variation of the torsional splittings with K(a) that has been observed experimentally.