This article focuses on convective instabilities of throughflow in packed beds with internal heat sources. When a packed bed is heated with internal heat sources, the effects of throughflow on the onset conditions of convection have been examined numerically under the linear stability theory. The resulting conditions show that stationary instabilities occur at higher values of Darcy-Rayleigh number than the critical values as the amount of throughflow increases. The effects of free and rigid boundaries on the onset condition are also obtained for the Brinkman porous media with throughflow.