Abstract This paper presents the calculation of rate coefficients for transitions between rotational levels of the A-type and E-type levels of methyl mercaptan (CH3SH) resulting from collisions with molecular hydrogen. Radiative transfer modeling requires both radiative and collisional rates to describe the rotational populations under the usual conditions in interstellar clouds where LTE conditions do not apply. To compute the intermolecular interaction between CH3SH and H2, the explicitly correlated CCSD(T)-F12a coupled-cluster method which utilized a correlation-consistent aug-cc-pVTZ basis was employed. The computed energies were fit to a functional form suitable for use in scattering calculations. Rate coefficients were calculated over the temperature range from 5 to 100 K for transitions between the 110 lowest CH3SH rotational levels (having energies less than 107 cm−1 (ca. 150 K) within both the A-type and E-type manifolds caused by collisions with para- and ortho-H2. The rate coefficients were obtained through time-independent quantum close coupling quantum scattering calculations utilizing the calculated PES.