A two-dimensional finite element based mathematical model of coupled turbulent fluid flow, heat transfer, and solidification in horizontal twin-roll thin strip casting was developed. Basic formulations for simulating the coupled thermal and flow fields are described in this paper. A k-ε turbulence model was used to calculate the turbulent viscosity in the melt pool. A variable viscosity model was used to model the mushy region. Inlet velocity, strip/roll heat transfer coefficient, alloy composition, and melt superheat were the main process variables considered. The effect of the above process variables on the sump depth, mean strip exit temperature, roll surface temperature, and temperature gradients inside the roll, was analyzed.