In this paper, we present a model characterizing the interaction of a radiative shock (RS) with a solid material, as described in a recent paper (Koenig et al., Phys. Plasmas, 24, 082707 (2017)), the new model is then related to recent experiments performed on the GEKKO XII laser facility. The RS generated in a xenon gas cell propagates towards a solid obstacle that is ablated by radiation coming from the shock front and the radiative precursor, mimicking processes occurring in astrophysical phenomena. The model presented here calculates the dynamics of the obstacle expansion, which depends on several parameters, notably the geometry and the temperature of the shock. All parameters required for the model have been obtained from experiments. Good agreement between experimental data and the model is found when spherical geometry is taken into account. As a consequence, this model is a useful and easy tool to infer parameters from experimental data (such as the shock temperature), and also to design future experiments.