A model is presented for the energy distribution of ions bombarding electrode surfaces in planar rf plasma reactors at low pressures, where collisions in the sheath may be ignored. Given the waveform for the voltage difference across the sheath adjacent to an electrode, the model predicts the ion bombardment energy distribution in the limits tr <1/f and tr ≫1/f, where tr is the transit time of the ions across the sheath and f is the frequency of the applied rf voltage. Utilizing sheath voltage waveforms from a previously published equivalent circuit model of a rf reactor [A. Metze, D. W. Ernie, and H. J. Oskam, J. Appl. Phys. 60, 3081 (1986)], the model shows that the ion bombardment energy distribution is bimodal and skewed toward lower ion bombardment energies. The model also demonstrates one of the mechanisms responsible for narrowing of the ion bombardment energy distribution with increasing rf frequency. These results are compared with experimental measurements.