A continuum model of deformation of a transform fault is considered. The fault interior is modelled as a part of a plate fragmented into a large number of angular blocks. The blocks are not joined together by any binder, but are rather held together due to external compression such that they can, in principle, rotate independently. Significant numbers of blocks involved in the deformation process permit a continuum description of the deformation, which in view of the possibility of independent rotations, necessitates the application of the Cosserat theory. The crucial point in the described model is the interconnection between the rotations and the normal stresses associated with the angular shape of the blocks: the rotating blocks `elbow' one another. Furthermore, elbowing produces compressive stresses independent of the direction of rotations. Consequently, the constitutive equations become non-linear involving absolute values of the components of the curvature tensor. The paper analyses a simple shear of a fault under constraining compression acting in the direction normal to the fault. An infinite layer subjected to opposite displacements and zero rotations at the edges is considered. It is shown that block rotations can lead to complex deformation patterns. There exists a displacement threshold proportional to the pressure: for imposed displacements below the threshold, the deformation pattern coincides with the conventional one as predicted for a classical elastic isotropic layer with uniform displacement gradient in the absence of block rotations. When the imposed displacement exceeds the threshold value, boundary zones of non-uniform rotations, displacement gradients and dilatation emerge. It is interesting to note that these features, which could be mistaken for indicators of non-elastic or localisation processes, occur in a situation where only elastic processes are acting at the scale of blocks and no friction or other energy dissipation processes take place.