The main objective of this PhD thesis is to develop a numerical model for the transient clogging process in submerged entry nozzle (SEN) during continuous casting. Three major steps of the clogging have been taken into account: (a) transport of non-metallic inclusions (NMIs) by turbulent melt flow towards the SEN wall; (b) interactions between melt and wall, and the adhesion of the NMI on the wall; (c) formation and growth of the clog by NMI deposition. The flow domain is treated differently for the bulk and near-wall regions. An Eulerian-Lagrangian approach is employed to calculate the transport of NMIs by the turbulent flow (bulk region); a stochastic near-wall model is adopted to trace particles in the turbulent boundary layer (near-wall region). The early stage of clogging is modeled by the dynamical change in wall roughness, while the late stage of the clogging is modeled by building layers deposited NMI particles in porous structure. This porous structure is called as ‘clog’, and it continues to grow by attaching more NMI particles. To evaluate the model, a laboratory experiment [Janis et al., Steel Res. Int. 86 (2015) 1271–1278], which was designed to study the clogging of SEN during steel continuous casting, is simulated. It is verified that the model can reproduce the experiment: the calculated clogged section of the nozzle is qualitatively comparable with as-clogged sections in laboratory experiments; the calculated mass flow rate through the nozzle agrees with the experimentally-monitored one as well. New knowledge is obtained. (1) Clogging is a transient process interacting with the melt flow; and it includes the initial coverage of the nozzle wall with deposited particles, the evolution of a bulged clog front, and then the development of a branched structure. (2) Clogging is a stochastic and self-accelerating process. Moreover, uncertainties for choosing the modeling parameters such as mesh size, Lagrangian time scale (T_L), the correction factor (n) in the interpolation of clog permeability are studied and discussed. Mesh size smaller than 0.1 mm in the near-wall region is recommended to have mesh independent results; the modeling result on particle deposition becomes insensitive to T_L and n when they are set at close to 6 μs and 5, respectively. The model is also evaluated for the industry process of continuous casting of steel, referring to the model accuracy and calculation efficiency. For the complex geometry of submerged entry nozzle (SEN), where it is not possible to create hexahedron mesh in the whole domain, a mixed mesh type is recommended, i.e. the wedge mesh for regions adjacent to SEN walls and the tetrahedron mesh for inner regions. Another challenge to the calculation of real SEN clogging is the huge number of particles as involved in the industry process. An artificial N-factor, where N is the number of NMIs each particle of Lagrangian frame represents, has to be introduced to reduce the calculation cost. A too large N-factor leads to calculation error. Therefore, a criterion is defined to limit the N-factor and ensure the modeling accuracy. As solidification of the steel melt on the SEN wall is also considered as a possible mechanism for clogging, the model is upgraded to be applicable for the non-isothermal conditions. The modeling results indicate that solidification should not occur in a SEN if the molten steel has sufficient superheat and it flows with relatively high speed through the SEN. However, clogging promotes the solidification inside the porous structure of clog. Finally, capabilities of the current state of the model from the numerical and practical point of views are discussed; the missing features or the functionalities which need future improvements are addressed.