  The existence of anisotropic stress of a purely geometrical origin seems to
be a characteristic of higher order gravity models, and has been suggested as a
probe to test these models observationally, for example in weak lensing
experiments. In this paper, we seek to find a class of higher order gravity
models of f(R,G) type that would give us a zero anisotropic stress and study
the consequences for the viability of the actual model. For the special case of
a de Sitter background, we identify a subclass of models with the desired
property. We also find a direct link between anisotropic stress and the
stability of the model as well as the presence of extra degrees of freedom,
which seems to be a general feature of higher order gravity models.
Particularly, setting the anisotropic stress equal to zero for a de Sitter
background leads to a singularity that makes it impossible to reach the de
Sitter evolution.
