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+2β T functional form, with β 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 d M/dρc >0 and sufficient condition ω2 >0, still hold in this theory of gravity.