Important problems that confront future scientific exploration of Mars include the physical properties of Martian surface materials and the geologic processes that formed the materials. The design of landing spacecraft, roving vehicles, and sampling devices and the selection of landing sites, vehicle traverses, and sample sites will be, in part, guided by the physical properties of the materials. Four materials occur in the sample fields of the Viking landers: (1) drift, (2) crusty to cloddy, (3) blocky, and (4) rock. The first three are soillike. Drift materials is weak, loose, and porous. We estimate that it has a dielectric constant near 2.4 and a thermal inertia near 1 ?? 10-3 to 3 ?? 10-3 (cal cm-2 sec 1 2 K-1) because of its low bulk density, fine grain size, and small cohesion. Crusty to cloddy material is expected to have a dielectric constant near 2.8 and a thermal inertia near 4 ?? 10-3 to 7 ?? 10-3 because of its moderate bulk density and cementation of grains. Blocky material should have a dielectric constant near 3.3 and a thermal inertia near 7 ?? 10-3 to 9 ?? 10-3 because of its moderate bulk density and cementation. Common basaltic rocks have dielectric constans near 8 and thermal inertias near 30 ?? 10-3 to 60 ?? 10-3. Comparisons of estimated dielectric constants and thermal inertias of the materials at the landing sites with those obtained remotely by Earth-based radars and Viking Orbiter thermal sensors suggest that the materials at the landing sites are good analogs for materials elsewhere on Mars. Correlation of remotely estimated dielectric constant and thermal inertias indicates two modal values for paired values of dielectric constants and thermal inertias near (A) 2 and 2 ?? 10-3 and (B) 3 and 6 ?? 10-3, respectively. These two modes are comparable to the dielectric constants and thermal inertias for drift and crusty to cloddy material, respectively. Dielectric constants and thermal inertias for blocky material are larger but conistent with values in the northern plains. Our interprertations are compatible with an aeolian origin for drift and similar materials elsewhere on Mars. The postulate that moderate dielectric constants and thermal inertias larger than 3 or 4 ?? 10-3 are produced by cementation of soillike materials is partly consistent with the data. The average dielectric constant and thermal inertia and their correlation with one another suggest that most of the surface of Mars should present few difficulties to future surface exploration, but some surfaces may present difficulties for spacecraft that are not suitably designed. ?? 1989.