A theory of fast‐ion generation in the 2XIIB mirror experiment due to a single resonant electrostatic ion‐cyclotron mode is presented. Assuming weak radial gradients of the magnetic induction, which appear to be consistent with experimental data, it is shown that ions with small parallel excursions can be accelerated into the 40 keV region. Allowance for a periodic temporal variation of the amplitude of the mode results in stochastic motion of those ions whose range of parallel excursions form a limited but significant fraction of the plasma length. The diffusion coefficients of this class of ions are computed in the quasilinear approximation. The corresponding diffusion times are in reasonable accord with those from the experiment.