An integrated macro/micro model is developed to represent the evolution of complex electrodynamic and transport phenomena and solidification microstructures in solidifying metals with electromagnetic stirring. The model development is based on the hybrid boundary/finite element solution of the Maxwell equations and the finite element (FE) solution of the momentum and thermal transport equations, in combination with the Monte-Carlo-cellular-automaton representation of the evolution of solidification microstructure formation. In applying the FE method for flow calculations, pressure is treated using the standard reduced penalty approximation and the phase interaction effects by the Carman-Kozney equation. A sub-level time and space scheme is developed to effectively integrate the macro- and micro-scale simulations. To enhance the computational speed, the microstructure formation-simulations are carried out in parallel using the Parallel Virtual Machine library. The model is applied to simulate the electrodynamic, fluid flow and heat transfer phenomena and microstructure formation in a Cavity surrounded by induction coils. Results show that magnetically induced stirring can have pronounced effects on the evolution of microstructure during solidification.