Solidification of a simple casting made of ductile iron is mathematically modeled in this work. The model is able to numerically simulate the cooling rate and solidification of the whole casting system composed by a cubic piece, a blind riser connected through a rectangular neck, and immersed in a green sand mold. The center of the neck acts as a valve that allows the flow of liquid metal between the casting and the riser based on the feeding technique known as Pressure Control Risering (PCR). The developed model couples the energy conservation equation and the solidification kinetics of ductile iron, through the statement of proper nucleation and growth laws. This model is satisfactorily validated by comparing the thermal histories predictions with experimental cooling curves obtained in the foundry laboratory for the same casting. According to a process analysis developed in this work, the pouring temperature is the variable that affects the most the solidification and the feeding behavior, since it increases significantly the solidification times in all regions of the casting system.