  Recent measurements of the out-of-plane magnetoresistance of delafossites
(PdCoO$_2$ and PtCoO$_2$) observed oscillations closely resembling the
Aharonov-Bohm effect. Here, we show that the magnetoresistance oscillations are
explained by the Bloch-like oscillations of the out-of-plane electron
trajectories. We develop a semiclassical theory of these Bloch-Lorentz
oscillations and show that they are a consequence of the ballistic motion and
quasi-2D dispersion of delafossites. Our model identifies the sample wall
scattering to be the most likely factor limiting the visibility of these
Bloch-Lorentz oscillations in existing experiments.
