The demand for large format round steel billet has been increasing in past decades. As a new casting method, semi-continuous casting (SCC) process, which attempts to combine the merits of ingot casting and continuous casting techniques, is becoming a competitive technique in modern steel plants to produce large round. However, understanding to the process regarding to the formation of as-solidified structure, macrosegregation, porosity, and so on is not very clear. The objective of this thesis is to use a three-phase columnar-equiaxed solidification model to simulate solidification process of SCC, evaluating the aforementioned issues and supplying instructive suggestions to the industry. This numerical model is originally developed by Wu and Ludwig [Metall. Mater. Trans. A, 2006, p.1613]. In order to model the SCC process, the numerical model was extended. Verifications of the extended model were made in several cases at different scales from laboratory benchmark to practical SCC strand. Following major numerical model extensions were made. 1) Consideration of transport of inoculants (embryos) in the melt. The inoculants serve as heterogeneous nucleation sites for the equiaxed crystals. The numbers of inoculants and equiaxed crystals are conserved. Inoculants move with liquid phase, while equiaxed crystals move with different velocity. 2) Consideration of the equiaxed-to-columnar transition (ECT) in the volume average model. The remaining melt can fully solidify as columnar structure when the available inoculants are consumed, resulting in ECT. 3) A new formula for crystal fragmentation. Based on the Flemings local remelting theory, it is the interdendritic flow in the columnar growth direction that promotes the solute enrichment of the local interdendritic melt, leading to the solute-driven remelting of the dendrite arms and the formation of crystal fragments. The extended model is validated against laboratory experiments. Validation of the fragmentation formula was made through the comparison with two benchmark experiments. The first one was based on a plate casting benchmark [Hachani et al., Int. J. Heat Mass Transfer, 85 (2015), p.438], as cast with Sn-10 wt.%Pb alloy and cooled laterally. The second one was an aqueous ammonium chloride (NH4Cl-H2O) experiment as cooled from top unidirectionally [Gao et al. in conf. MCWASP VIII, 1998, p.425]. Simulation results agreed quantitatively and qualitatively with observations from experiments. The extended model was implemented into industrial-scale casting processes. The model with extended features for inoculant-equiaxed crystal conservation and ECT was implemented into a simulation case of vertical continuous casting (VCC). The predicted macrosegregation along the diameter agrees well with the experimental measurement from the plant trial. The model with extended features for fragmentation and magnetic stirring (EMS) was incorporated into the semi-continuous casting (SCC) process. Reasonable results were obtained. It can be concluded that the extended three-phase mixed columnar-equiaxed solidification model can be used to study the casting process of industry scale, such as SCC and VCC. The model was partially validated against laboratory experiments and limited industry trial. Further validations are desirable.