A simple model potential is proposed to describe the dynamical barrier in the mean interaction potential at small distances between the reactants in S(1D) + HD(1Σ, v = 0, j = 0) reaction. The statistical theory of collision complex formation and complex decay is applied to calculate the total reaction cross sections and the cross sections for SH and SD productions in the range of low collision energies Ec = (0.4-60) meV. The results are compared with measured cross sections and results of hyperspherical close coupling calculations. As a check of consistency the same comparisons are presented for the case of S(1D) + H2(1Σ, v = 0, j = 0) reaction.