In the present study, the optimal design of feeding system in steel sand-mold castings is considered. The first part of this research includes fundamental studies on the physics of shrinkage defect formation during the casting process. The results of these studies lead to new findings on the mechanism of shrinkage defect formation, effect of melt quality on the distribution of defects within the castings and the connection between shrinkage and gases defects. The theoretical analysis of thermal criterion functions for the prediction of shrinkage defects in castings and introducing new criterion function with fewer shortcomings can be accounted as the other finding of this part. A new model was introduced in the second part of this research for the purpose of optimal design of feeding system in the shape casting processes. In this model the optimal design problem is formulated as a point-wise constrained topology optimization problem. Unlike alternative methods, the presented method does not require any predesigned feeding system as an initial guess. Using the functional analysis on the infinite-dimensional function spaces, a numerically efficient method was introduced to solve the optimal design problem in this study. By using extensive numerical experiments, capabilities and limitations of the presented method were studied in the last part of this research.