We report the results of coupled channels calculations of cross-sections for torsionally elastic and inelastic transitions in E-type methanol (CH3OH), with helium as the colliding partner. The dependence of the CH3OH-He interaction potential on the internal rotation (torsional) angle was determined using second-order many-body perturbation theory. The methanol basis comprised levels belonging to the ground torsional state (nu = 0) and the first excited torsional state (nu = 1). The collisional 'propensity rules' observed in the case of torsionally elastic collisions were found not to apply to torsionally inelastic transitions between states of nu = 0 and 1. We assessed the effect of the torsional coupling on the torsionally elastic cross-sections and found changes of no more than about 30% at the highest collision energy considered (500 cm(-1)). The cross-sections for torsionally inelastic transitions were found to be typically two orders of magnitude smaller than for torsionally elastic transitions.