A formalism is developed for numerically calculating reflection and absorption of right‐hand polarized waves and reflection of left‐hand polarized waves propagating into a cyclotron resonance zone in a medium in which both magnetic field and plasma density are varying. The results are shown to agree with previous analytic calculations in the limit of constant density, weak collisionality, and linearly varying magnetic field, where the analytic calculation applies. The formalism is then applied to a plasma with general field and density variations, and arbitrary collisionality. The absorption and reflections are calculated for various boundary conditions along the propagation path, showing that there is an optimum density for power absorption. The collisionless absorption in the resonance zone, calculated from the single particle heating averaged over the flux is shown to be consistent with the linear wave absorption at low absorption and collisionality. At high absorption a prescription for bringing the two calculation methods into agreement is advanced. The results are used to qualitatively explain some previously puzzling experimental observations.