Metal composite parts are widely used in different industries owing to their significant improvement in material properties, such as mechanical strength, electrical conductivity, and corrosion resistivity, compared to traditional single metals. Such composite parts can be manufactured and processed in different ways to achieve the desired geometry and quality. Among various metal forming techniques, drawing is the most commonly used process to produce long composite wires or rods from raw single materials. During the drawing process of composite wires or rods, not only does the core radius ratio change, but the core or sleeve layer may also undergo necking or fracture due to excessive tensile stresses in the softer layer. In this paper, bimetallic rods with AISI-1006 low-carbon steel cores and C10100 oxygen-free electronic copper sleeves are modeled using the finite element software DEFORM. The simulation models are verified by drawing experiments. The effects of initial bonding conditions, the initial core ratio, reduction ratio, semi-die angle, drawing speed, and friction on the plastic deformation behavior of the bimetallic rods are investigated. The results indicate that the initial bonding conditions have a great impact on the deformation behavior of the billets in terms of strain distribution, material flow, residual stress, and the final core ratio. The permissible forming parameters for obtaining a sound product are investigated as well. With the aid of these analyses, the drawing process and the quality of the products can be controlled steadily.