Measurements were made of the orientation dependence of the Knoop microhardness H(K) on the (001) and (110) faces of single crystals of red (tetragonal) mercuric iodide that were vapour-grown for use in radiation detectors. The (001) faces of the crystals are softest when the major diagonal of the Knoop indentor (called here "the indentor") is parallel to the [100] crystallographic axis, and H(K) increases monotonically, by about 25%, as the indentor is rotated from the [100] to the [110] axis. The (110) surfaces are hardest when the indentor is parallel to [001]; H(K) decreases by about 50% as the indentor is rotated from [001] to [110BAR]; the experimental data indicate an intermediate microhardness minimum that occurs before the [110BAR] orientation is reached. Particularly interesting surface topography, including bands of slip lines, is observed in the vicinity of indentations on the (110) planes, which apparently have not previously been characterized by Knoop microhardness indentation. Theoretically, the size of a microhardness indention is presumed to depend on the volume of material in which appropriate slip systems are stressed sufficiently to cause appreciable slip. To test this concept and determine which particular slip systems dominate the indention process, the "infinite flat punch" model was used to calculate the orientational and volumetric variations of shear stress on various potential slip systems in mercuric iodide. For indention processes controlled by movement (i.e. slip) of material in the [001] direction, over {100} planes, these calculations predict the following (experimentally observed) results : (a) on the (001) plane, H(K) is smallest at [001] and greatest at [110], with no intermediate extremum; (b) on the (110) plane, H(K) has its greatest value at [001] and a minimum between [001] and [110BAR]; (c) H(K) at [110] on the (001) plane is essentially the same as H(K) at [110BAR] on the (110) plane; and (d) the relative variation of H(K) is greater on the (110) than on the (001) surface. Finally, the expected orientational variation of H(K) on the (100) and (101) surfaces was determined theoretically.