A unified model of an induction-stirred ladle in two and three dimensions is presented. Induction stirring of molten steel is a coupled multiphysics phenomena involving electromagnetic and fluid flow. Models presented in this paper gives a more accurate description of the real stirring conditions and flow pattern by taking into account the multiphysics behavior of the induction-stirring process in an induction-stirred ladle. This paper presents formulation of coupled electromagnetic and fluid flow equations. The coupled electromagnetic and fluid flow equations are solved with the use of the finite element method in two and three dimensions. The model is used to predict values of steel velocities and magnetic flux density. The model is also used to predict the effect of increased current density on flow velocity. Magnetic flux density values obtained from the model are verified against the experimental values. Copyright © 2012 John Wiley & Sons, Ltd.