An atomistic simulation of the structural properties of the new ternary A4Rh13Si9 and A4Ir13Si9 compounds, where A is Th, U, has been carried out using interatomic pair potentials based on the lattice inversion method. The calculated lattice parameters are corresponding to the experimental results. The phase stability of the intermetallics A4Rh13Si9 and A4Ir13Si9 is tested by high temperature disturbance under the control of the pair potentials. Moreover, the phonon densities of states, specific heat and vibrational entropy related to dynamic phenomena are evaluated for the first time. The method utilized in the present investigation offers a rather easy and direct way to study the structural and vibrational properties of A4Rh13Si9 and A4Ir13Si9.