  We examine the static structure configurations and radial stability of
compact stars within the context of $f(R, T)$ gravity, with $R$ and $T$
standing for the Ricci scalar and trace of the energy-momentum tensor,
respectively. Considering the $f(R, T)=R+2\beta T$ functional form, with
$\beta$ being a constant, we derive the corresponding hydrostatic equilibrium
equation and the modified Chandrasekhar's pulsation equation. The mass-radius
relations and radial mode frequencies are obtained for some realistic equations
of state. Our results show that the traditional stellar stability criteria,
namely, the necessary condition $dM/d\rho_c >0$ and sufficient condition
$\omega^2 >0$, still hold in this theory of gravity.
