This thesis work concerns about the importance of the cast surfaces, surface phenomenon such as the formation of the oscillation marks and exudation and related defects including cracks and segregation that happened during the continuous casting. All of the investigated materials were collected during the plant trials while an in-depth analysis on these materials was performed at the laboratory scale with certain explanations supported by the schematic and theoretical models. The work consists on different material classes such as steels and phosphor bronzes with a focus on the surface defects and their improvements. In order to facilitate the theoretical analysis which could be capable of explaining the suggested phenomenon in the thesis, a reduced model is developed which required lesser computational resources with lesser convergence problems.