In the past, most information on the plasticity of rocks has been derived from axisymmetric compression experiments. These data are the basis for Arrhenius-type flow laws which relate stress and strain, treating them essentially as scalars and not accounting for the deformation history. This assumption is valid for a very limited range of mechanisms, for example, superplastic flow, dislocation climb, and some mechanisms of recrystallization. Wherever dislocation glide is involved in the deformation process, preferred orientation develops which depends on the strain mode. The development of texture has a profound influence on the stress-strain curve: (1) a geometric factor due to crystal orientation and expressed by the Taylor factor, (2) strain hardening due to interaction of dislocations in active slip systems, and (3) latent hardening because of microstructural difficulties in activating inactive slip systems at expected critical shear stresses. We have analyzed the influence of geometric factors on the plasticity of calcite polycrystals using the full constraint Taylor theory and observed that effects of strain mode are even stronger than in metals where the anisotropy of plastic flow was first documented. For example, at low temperature in axial deformation the specimen hardens rapidly, whereas in plane strain it softens during straining. The differences can be attributed to activation of different slip systems (number and relative importance) in each case, particularly the role of mechanical twinning. Wherever dislocation glide is significant, anisotropic flow laws should be considered, also in geological materials, to explain deformation. Particularly emphasized is the importance of deformation experiments in geometries different from axisymmetric compression.