Physical processes involved in collisionless damping of the fast hydromagnetic mode are investigated by considering the stochastic heating of electrons by a random spectrum of fast waves. We take as a model a weakly damped fast wave, propagating in a direction such that the damping is mainly due to electron heating; allowance is made for the possibility of a small component of electric field parallel to the unperturbed field. To estimate the damping we consider an ensemble of electrons accelerated (1) by magnetic‐moment magnetic‐field‐gradient interaction and (2) by the parallel electric field. Electron heating is calculated from a Fokker—Planck type of equation; the damping decrement is obtained by equating the electron heating rate to the wave energy loss rate, and agrees with the damping decrement obtained from the appropriate asymptotic limit of the general dispersion relation. Some general aspects of this method for obtaining wave‐damping decrements are discussed.