We examine the optical resonator composed of two astigmatic elements, in a twisted configuration. These cavities have mode cross-sections with principal axes that rotate on propagation. Explicit cavity mode equations are derived for the case of identical mirrors. Such a resonator is appropriate for a solid-state laser that is end-pumped with the output of a laser-diode array brought to a line focus. We present a simple analysis of the significance of rotational misalignment, which effects the pump-to-mode power coupling, beam quality, and cavity stability.