One-dimensional semiclassical transition state theory is applied to study the rate constants of the CH3 + CH4 reaction and its hydrogen-substituted isotopic analogues. This requires calculation of vibrational frequencies at the reactant, product and transition states, and the anharmonic constants of the reaction coordinate at the transition state. The reactions studied have a hindered rotor vibration at the transition states, whose behaviour is approximated using two methods. The results show very good agreement to experimental and other theoretical results. The three reactions studied allow evaluation of both primary and secondary kinetic isotope effects in the title reaction. (C) 2018 Elsevier B.V. All rights reserved.