An accurate modeling of solidification and melting in optically thick media requires equations for heat conduction and radiation along with constitutive relations for phase change. In the present study, the problem is described by the heat equation subject to the enthalpy approach. To incorporate radiation effects into the model, we consider a simplified \(\mathrm {P}_1\) approximation of the radiative transfer equation. The numerical solution of the governing equations is performed by an implicit time integration method using finite element discretization. The method is accurate and stable for a wide range of optical scales and Stefan numbers. In addition, the implicit treatment in the method eliminates most of the numerical difficulties that usually appear in the explicit methods for phase change problems. Numerical results are presented and comparisons between simulations with and without radiation are also illustrated for two examples of solidification and melting in optically thick media.