Interest in the mechanical properties of water ice under the conditions in which it exists in the outer solar system has motivated the development and use of a new high‐pressure, low‐temperature triaxial deformation apparatus. Constant displacement rate tests on 70 samples of pure polycrystalline water ice have been performed at temperatures 77≤≤258 K, confining pressures 0.1≤≤350 MPa, and strain rates 3.5×10≤ ≤3.5×10 s. In most cases, the ice polymorph tested was ice . Both brittle and ductile behavior have been observed. Brittle behavior of ice, promoted by lower pressure, lower temperature, and higher strain rate, is analogous to that in rocks, with the important exception that brittle fracture strength becomes independent of confining pressure above 50 MPa pressure and the fracture angle is approximately 45° to the loading direction (i.e., the coefficient of internal friction is approximately zero). Ductile flow, the predominant behavior in our tests at ≥195 K, follows a law of form = σ exp (−*/) (σ is stress; is the gas constant; , * are material constants). Three sets of material constants are required to fit the data, with changes in sets (or mechanisms) occurring near 243 K and 195 K. The value of remains near 4 throughout the measured ductile field, but * drops from 91 to 61 to 31 /mole as temperature decreases. The maximum brittle strength measured was 171 MPa; the maximum ductile strength measured was 91 MPa. At confining pressures near the phase transition pressure of ice → ice II, the ductile strength is observed to drop dramatically. Some overlap with previous work occurs at higher temperatures and lower pressures. Agreement with present work is generally good, both quantitatively in the values of and *, and qualitatively in the mechanism of deformation. Although the ductile strengths measured here are somewhat higher than expected on the basis of extrapolations of previous work, the low value of * at <195 K indicates that the ice layer on icy bodies in the solar system is much weaker than has generally been predicted.