  We consider conditions for existence and stability of a static cosmological
solution in quadratic gravity. It appears that such a solution for a Universe
filled by only one type of perfect fluid is possible in a wide range of the
equation of state parameter $w$ and for both positively and negatively
spatially curved Universe. We show that the static solution for the negative
curvature is always unstable if we require positive energy density of the
matter content. On the other hand, a static solution with positive spatial
curvature can be stable under certain restrictions. Stability of this solution
with respect to isotropic perturbation requires that the coupling constant with
the $R^2$ therm in the Lagrangian of the theory is positive, and the equations
of state parameter $w$ is located in a rather narrow interval. Nevertheless,
the stability condition does not require violation of the Strong Energy
Condition. Taking into account anisotropic perturbations leads to further
restrictions on the values of coupling constants and the parameter $w$.
