Abstract. Muon radiography is a technique that uses naturally occurring showers of muons (penetrating particles generated by cosmic rays) to image the interior of large scale geological structures in much the same way as standard X-ray radiography is used to image the interior of smaller objects. Recent developments and application of the technique to terrestrial volcanoes have demonstrated that a low-power, passive muon detector can peer deep into geological structures up to several kilometers in size, and provide crisp density profile images of their interior at ten meter scale resolution. Preliminary estimates of muon production on Mars indicate that the near horizontal Martian muon flux, which could be used for muon radiography, is as strong or stronger than that on Earth, making the technique suitable for exploration of numerous high priority geological targets on Mars. The high spatial resolution of muon radiography also makes the technique particularly suited for the discovery and delineation of Martian caverns, the most likely planetary environment for biological activity. As a passive imaging technique, muon radiography uses the perpetually present background cosmic ray radiation as the energy source for probing the interior of structures from the surface of the planet. The passive nature of the measurements provides an opportunity for a low power and low data rate instrument for planetary exploration that could operate as a scientifically valuable primary or secondary instrument in a variety of settings, with minimal impact on the mission's other instruments and operation.