The effect of the number and orientation of available slip systems on the indentation of model planar single crystals is investigated. The crystal is taken to have three slip systems oriented at 60° relative to each other. The material is characterized by viscoplastic continuum slip theory. The number of potentially active slip systems is controlled by specifying values of the flow strength on each of the systems. Attention is confined to indentation of a block by a sticking rigid sharp indenter. Crystals with one, two or three soft (and therefore potentially active) slip systems are considered. We also investigate the effect of the orientation of the soft slip system relative to that of the indenter. Results are presented for the hardness, the mode of slip, the induced lattice rotations and the stress distribution. The relation between the nominal indentation hardness and the slip system strength depends on the number of soft slip systems and can differ significantly from that for a plastically isotropic solid. With two or three soft slip systems, circumstances are found where the deformation mode involves regions of predominantly single slip. Particularly when there is one soft slip system, regions of positive mean normal stress can develop, the location of which depends on the orientation of the soft slip system relative to the indenter.