As energy efficiency increases in importance, researchers have identified manufacturing processes as opportunities where energy consumption can be reduced. Drawing is one widely employed, energy intensive manufacturing process, which could benefit by analysis of energy consumption during operation. To optimize the energy consumption of the drawing process, this paper developed an explicit model to quantify the process energy for the cylindrical drawing process by analyzing the dynamic punch force during the process. In this analysis, the evolution of the stress and strain was analyzed in the drawn part by considering all the structure parameters of the drawn part. The stress and strain analyses were integrated into an overall process energy model, and the behavior of the model was classified into three categories, based on their physical mechanisms, i.e., deformation energy, bending energy, and friction energy. The model was validated using numerical experiments designed by the Taguchi method where two different kinds of materials were tested over 18 runs. The results from the numerical experiments were compared with those from the model, and show that the maximum variation of the process energy predicted by this model is less than 10% for a given part. Sensitivity analysis was performed on the model to understand the contributions of the process parameters on the process energy to guide process optimization for lower energy consumption. The established model can assist in the rapid design of drawn parts with lower embodied energy.