A computer programme has been developed for analyzing the two-dimensional, unsteady conservation equations for transport phenomena in the molten region of twin-roll continuous casting in order to describe the velocity, and temperature fields, and the solidification process of the molten steel. The energy equation of the cooling roll is solved simultaneously with the conservation equations of molten steel in order to consider heat transfer through the cooling roll. The governing equations are expressed in the generalized coordinates to consider the characteristics of a rotating bank between twin-rollers. In the molten region, it is predicted that transient recirculating flows with small and large vortices are located in the vicinity of the middle of the twin-rollers. The temperature field is affected by the flow fields, showing the complete two-dimensional pattern. The solidification pattern in the molten steel and the temperature distribution in the cooling roll are also obtained as a function of time.