The transition zone is the region in the Earth's mantle between 410 and 660 km depth that separates the upper from the lower mantle. In spite of its small volume, it may play a role in constraining the style, vigour and scale of global mantle convection through, for instance, the fate of subducting slabs. Mantle convection is governed by plastic flow that occurs through the motion of crystal defects. Line defects or dislocations are considered to be one of the most efficient defects contributing to intracrystalline deformation. That is why in this work, we concentrate on the motion of dislocations in relation to the major phases of the mantle transition zone: wadsleyite and ringwoodite. A theoretical mineral physics approach is used to model the thermally activated glide motion of dislocations at appropriate pressure conditions in both high-pressure polymorphs of olivine. The intrinsic properties of dislocation core structures are modelled and parametrized by atomic scale calculations to take into account the effect of pressure on atomic bonding. Plastic deformation is finally described by taking into account the instrinsic strain rate dependence on the mobility of the defects.Since plastic deformation by the motion of dislocations is associated with creep, we use the above results and a climb mobility law to address the effective creep process in wadsleyite and ringwoodite under natural conditions. We show the inefficiency of dislocation glide as a strain producing deformation mechanism and suggest the potential importance of pure climb creep in the main minerals constituting the Earth's transition zone. This would imply the mantle transition zone to be rheologically distinct from the upper mantle.