In this paper we have investigated two fluid axially symmetric cosmological models in $f(R, T)$ theory of gravitation. To get the deterministic model, we have assumed a supplementary condition $H_3=k H_1$, where $H_1$ and $H_3$ are Hubble parameters and $k$ is constant. Two-fluid model in $f(R, T)$ theory of gravitation, one fluid represents the matter content of the universe and another fluid is chosen to model the cosmic microwave background radiation. Some geometric aspects of the model are also discussed.