The pressure-volume relationships for superconductors near absolute zero are of potential interest for comparison with theories which attempt to explain the variation of the superconducting transition temperature with pressure. Such data for thallium are of special interest since the variation of transition temperature with pressure is different for thallium than for any other known pure metal. In these experiments, measurements on indium of the total compression to 10 000 atmos for various temperatures down to 4.2°K served as a check of similar measurements on thallium. No unusual behavior was found for either metal. These results were combined with the measurement of the total thermal expansions for both metals to give isobars at both zero pressure and at 10 000 atmos pressure over the range from 4.2° to 300°K. The results of some low-temperature compressive testing experiments on both metals are also given, together with some indirect evidence as to the vanishing of work hardening effects at low temperature and moderate hydrostatic pressures. Finally, measurements on the electrical resistance of indium show an unexplained kink in the R vs T curve at about 210°K. The effect on the electrical resistance of indium due to tensile (plastic) deformation at 4.2°K was also measured.