We surveyed the subsurface structure of Chryse and Acidalia Planitiae using data from the Mars SHAllow RADar sounder (SHARAD) onboard the Mars Reconnaissance Orbiter (MRO). Several subsurface reflectors were identified in these regions, but these reflectors do not constitute apparent subsurface structures larger than 30 km. The bulk dielectric constants of the uppermost layers at two locations were estimated as 5.3 and 5.9 from the combination of high-resolution images and topographic data. These values were used to constrain the possible bulk porosity (approximately 28 % and 25 %) and the upper limit for the volume fraction of water ice (~43 % and ~50 %). The estimated porosities of the shallow subsurface layers in these locations can be explained by the emplacement of basaltic rock or till that may contain some ice-cemented regolith.