The Shallow Radar (SHARAD) on the Mars Reconnaissance Orbiter has imaged the internal stratigraphy of the north polar layered deposits of Mars. Radar reflections within the deposits reveal a laterally continuous deposition of layers, which typically consist of four packets of finely spaced reflectors separated by homogeneous interpacket regions of nearly pure ice. The packet/interpacket structure can be explained by approximately million-year periodicities in Mars’ obliquity or orbital eccentricity. The observed ~100-meter maximum deflection of the underlying substrate in response to the ice load implies that the present-day thickness of an equilibrium elastic lithosphere is greater than 300 kilometers. Alternatively, the response to the load may be in a transient state controlled by mantle viscosity. Both scenarios probably require that Mars has a subchondritic abundance of heat-producing elements.