  This thesis has considered the existence of anisotropic exact vacuum
solutions in the context of higher order gravities. The investigated models
generally are a function of three scalars R, $R_{\alpha\beta}R^{\alpha\beta}$
and $R_{\alpha\beta\mu\nu}R^{\alpha\beta\mu\nu}$. Near singularity, dominant
terms in the expansion of analytic type of these functions are in terms of
$R^{n}$ (practically $R^{1+\delta}$, for indicating deviation from
Einstein-Hilbert action), ($R_{\alpha\beta}R^{\alpha\beta})^{n}$ or
($R_{\alpha\beta\mu\nu}R^{\alpha\beta\mu\nu})^{n}$. Investigation shows that
there always exists Kasner type solutions in $R^{n}$ and
$R_{\alpha\beta}R^{\alpha\beta})^{n}$ models. But, in the third type model,
anisotropic Kasner type solution has not been found. Furthermore, the behavior
of these models in the presence of matter has been investigated, and it has
been revealed that these solutions are always valid for relativistic matter,
however this is not true for some non relativistic matter. Moreover, the energy
condition for $R^{1+\delta}$ model in vacuum has been investigated and has been
shown that the application of four energy conditions (weak, null, strong and
dominant) leads to one constraint on $\delta$.
