Based on twin-roll casting technology and multi-roll groove rolling technology, a Multi-Roll Solid-Liquid Cast-Rolling Bonding (MRSLCRB) process was proposed to fabricate Cu/steel cladding bars, which processes the advantages of short flow and high-efficiency. However, it is a typical 3-D thermal-fluid-mechanics coupled problem, and determining cast-rolling force is difficult during the equipment design. Therefore, the geometrical evolution of the cast-rolling area was studied, laying the foundation to establish contact boundary equations and analyze mechanical schematics and metal flow. Then, a 3-D steady-state thermal-fluid coupled simulation model, including casting roll, substrate bar, and cladding metal, was established. The Kissing Point (KP) height, average outlet temperature, and process window were predicted, and simulation results of the three-roll layout indicate that the KP distribution along the circumferential direction can be considered uniform. Hence, the engineering cast-rolling force model was derived based on the differential element method and plane deformation hypothesis. The accuracy was verified by the 3-D finite element model, and the influences of process layouts and technological parameters on the cast-rolling force were analyzed. Through the indirect multi-field coupled analysis method, the temperature–pressure evolution and reasonable process window can be predicted, which provides a significant basis for guiding equipment design and improving product quality.