SUMMARYThe twin-roll process is modelled by a coupled fluid flow and phase change model by means of a versatile finite element method. Here, a simple numerical scheme is proposed to solve the problem of determining the interface shape under the thermal equilibrium condition. The procedure is based on a finite element method using a transform technique. The simple numerical method provides an efficient and accurate way to find the interface position and shape with arbitrary boundary geometry. This method can easily be implemented on the existing finite element program, and provides a simple and efficient tool to simulate the solidification as well as the fluid flow problem of the twin-roll casting process.