  In the model of solid / elastic inflation, inflation is driven by a source
that has the field theoretical description of a solid. To allow for prolonged
slow roll inflation, the solid needs to be extremely insensitive to the spatial
expansion. We point out that, because of this property, the solid is also
rather inefficient in erasing anisotropic deformations of the geometry. This
allows for a prolonged inflationary anisotropic solution, providing the first
example with standard gravity and scalar fields only which evades the
conditions of the so called cosmic no-hair conjecture. We compute the curvature
perturbations on the anisotropic solution, and the corresponding
phenomenological bound on the anisotropy. Finally, we discuss the analogy
between this model and the f (phi) F^2 model, which also allows for anisotropic
inflation thanks to a suitable coupling between the inflaton phi and a vector
field. We remark that the bispectrum of the curvature perturbations in solid
inflation is enhanced in the squeezed limit and presents a nontrivial angular
dependence, as had previously been found for the f (phi) F^2 model.
