Many constitutive laws for the flow of ice have been published since the advent of the Voyager explorations of the outer solar system. Conflicting data have occasionally come from different laboratories, and refinement of experimental techniques has led to the publication of laws that supersede earlier ones. In addition, there are unpublished data from ongoing research that also amend the constitutive laws. Here we compile the most current laboratory-derived flow laws for water ice phases I, II, III, V, and VI, and ice I mixtures with hard particulates. The rheology of interest is mainly that of steady state, and the conditions reviewed are the pressures and temperatures applicable to the surfaces and interiors of icy moons of the outer solar system. Advances in grain-size-dependent creep in ices I and II as well as in phase transformations and metastability under differential stress are also included in this compilation. At laboratory strain rates the several ice polymorphs are rheologically distinct in terms of their stress, temperature, and pressure dependencies but, with the exception of ice III, have fairly similar strengths. Hard particulates strengthen ice I significantly only at high particulate volume fractions. Ice III has the potential for significantly affecting mantle dynamics because it is much weaker than the other polymorphs and its region of stability, which may extend metastably well into what is nominally the ice II field, is located near likely geotherms of large icy moons.¿ 1997 American Geophysical Union