  In the present paper an attempt has been made to study the spatially
homogeneous and isotropic FRW model and axially symmetric spacetime in f(R)
theory of gravity. We have obtained the solutions of the field equations in
vacuum. To find the solutions of axially symmetric space-time we have assumed
the relation between scale factor and scalar field and also we considered that
scalar expansion ({\theta}) in the model is proportional to shear scalar
({\sigma}). The physical behavior for both models have been discussed by using
physical parameters. The function of Ricci scalar is investigated for these
models. Key words: f(R) theory of gravity, FRW universe, Axially symmetric
space-time.
