  The implications from the existence of a proper Homothetic Vector Field (HVF)
on the dynamics of vacuum anisotropic models in $F(R)$ gravitational theory are
studied. The fact that \emph{every} Spatially Homogeneous vacuum model is
equivalent, formally, with a "flux" -free anisotropic fluid model in standard
gravity and the induced power-law form of the functional $F(R)$ due to
self-similarity enable us to close the system of equations. We found some new
exact anisotropic solutions that arise as fixed points in the associated
dynamical system. The non-existence of Kasner-like (Bianchi type I) solutions
in proper $F(R)-$gravity (i.e. $R\neq 0$) strengthens the belief that curvature
corrections will prevent the shear influence into the past thus permitting an
isotropic singularity. We also discuss certain issues regarding the lack of
vacuum models of type III, IV, VII$_{h}$ in comparison with the corresponding
results in standard gravity.
