In this paper conduction-radiation controlled solidification process of semitransparent materials was numerically analyzed. New approach in this kind of simulations, which is based on the fixed grid front tracking method combined with the immersed boundary technique, was adopted and examined. The presented method enables accurate dealing with solidification processes of semitransparent materials which have different optical and thermophysical properties of solid and liquid phases as well as with absorption, emission, and reflection of the thermal radiation at the solid-liquid interface without applying moving mesh methods. The proposed numerical approach was examined by solving several simplified thermal radiation problems with complex fixed and moving boundaries both in two-dimensional and axisymmetric spaces. For some of them the accuracy of obtained results was proved by comparing with reference works, other showed capabilities of the proposed method. For simplified solidification processes of semitransparent materials three configurations of optical properties, i.e., semitransparent solid phase and opaque liquid phase, opaque solid phase and semitransparent liquid phase, and semitransparent both phases were considered. The interface between solid and liquid phases was treated to be opaque, absorbing, emitting, and reflecting diffusely the thermal radiation. Results of the numerical simulations show that the presented numerical approach works well in this kind of problems and is promising for simulation of real solidification processes of semitransparent materials.