  The main purpose of this paper is to investigate the exact solutions of
cylindrically symmetric spacetime in the context of $f(R,T)$ gravity [1], where
$f(R,T)$ is an arbitrary function of Ricci scalar $R$ and trace of the energy
momentum tensor $T$. We explore the exact solutions for two different classes
of $f(R,T)$ models. The first class $f(R,T)=R+2f(T)$ yields a solution which
corresponds to an exterior metric of cosmic string while the second class
$f(R,T)=f_1(R)+f_2(T)$ provides an additional solution representing a non-null
electromagnetic field. The energy densities and corresponding functions for
$f(R,T)$ models are evaluated in each case.
