As the product quality requirements are ever increasing and the gains in productivity are a must to sustain the competition, numerical modeling is now an essential tool to reach these targets. Due to the complexity of continuous and DC casting processes, a coupled multi-physics approach is required to capture all the important phenomena. This paper will present a fully coupled thermal-flow-transport-stress 3D modeling of continuous casting processes, with illustrations on continuous casting of steel and DC casting of aluminum. The influence of fluid flow, using different nozzle designs, on the first solidified shell will be investigated, together with the stress build-up and the air gap formation. Such coupling is achieved using a novel technique recently developed based upon the Mixed Lagrangian-Eulerian method (MiLE) implemented in the Finite Element software ProCAST. Finally, results of microporosity, grain structure and solid state transformations, based upon further multi-physics coupling, will be presented.