Olivine single crystals have been deformed under high confining pressure (P=5 GPa) and temperature (T=1400 degrees C) conditions in a multi-anvil high pressure apparatus. NaCl, diamond and NaCl + diamond (2 : 1 by volume) powders were encapsulated along with the olivine single crystals in order to produce a range of stress states. The change of the non-hydrostatic stress transmitted to the olivine samples, enclosed within these three different media, during heating has been evaluated by observation of dislocation microstructure and density. A higher differential stress can be generated with diamond powder (0.1 GPa) than with NaCl powder (0.02 GPa). Although an intermediate differential stress between 0.1 GPa and 0.02 GPa had been expected to be generated using NaCl + diamond powder, the generation of non-hydrostatic stress in the olivine sample was unsuccessful. This may be caused by the fact that compaction (or sintering) proceeded in the capsule throughout the experiments. The most important finding of these experiments is that a constant non-hydrostatic stress can be applied to a sample under very high pressure and temperature conditions within the multi-anvil high pressure apparatus for the duration of the experiment. This approach is therefore suitable for investigating the steady-state rheological properties of mantle minerals at near-mantle conditions.