For technical reasons, virtually all plastic deformation experiments on geological materials have been performed in either pure shear or simple shear. These special case loading geometries are rather restrictive for those seeking insight into how microstructure evolves under the more general loading geometries that occur during natural deformation. Moreover, they are insufficient to establish how plastic flow properties might vary with the 3rd invariant of the deviatoric stress tensor (J3) which describes the stress configuration, and so applications that use those flow properties (e.g. glaciological and geodynamical modelling) may be correspondingly compromised. We describe an inexpensive and relatively straightforward modification to the widely used Paterson rock deformation apparatus that allows torsion experiments to be performed under simultaneously applied axial loads. We illustrate the performance of this modification with the results of combined stress experiments performed on Carrara marble and Solnhofen limestone at 500°–600 °C and confining pressures of 300 MPa. The flow stresses are best described by the Drucker yield function which includes J3-dependence. However, that J3-dependence is small. Hence for these initially approximately isotropic calcite rocks, flow stresses are adequately described by the J3-independent von Mises yield criterion that is widely used in deformation modelling. Loading geometry does, however, have a profound influence on the type and rate of development of crystallographic preferred orientation, and hence of mechanical anisotropy. The apparatus modification extends the range of loading geometries that can be used to investigate microstructural evolution, as well as providing greater scope for determining the shape of the yield surface in plastically anisotropic materials.