Torsional vibrations of a sulfoxylic acid molecule (HOSOH) and its two deuterated isotopologues were analyzed for the first time. Harmonic and anharmonic calculations of the vibrational frequencies of the trans- and cis-conformers were performed. More rigorous consideration of the torsional vibrations was made based on 2D potential energy and kinematic coefficient surface calculations. These calculations were made at the MP2/cc-pVTZ and MP2/cc-pVQZ levels of theory, and then the results were extrapolated to the complete basis set limit. The 2D surface of the zero-point vibrational energy of a sulfoxylic acid molecule was calculated at the MP2/cc-pVTZ level of theory in anharmonic approximation and taken into account. The energies of the torsional states were found by numerical solution of the vibrational Schrodinger equation of the restricted dimensionality using the Fourier method. 2D surfaces of the dipole moment components were calculated too. Using all these data, the torsional IR spectra of the trans- and cis-conformers of the HOSOH, DOSOD, and DOSOH molecules were also modeled at different temperatures.