Incremental sheet forming (ISF) has emerged as one of the rapid prototyping processes in forming 3D-shaped products from design data without much need for human and tool intervention. Past studies show that an extensive focus has been paid on the analysis of surface roughness, clamped accuracy, and energy consumption in terms of machine standby and positioning energy, while very little focus was paid to deformation energy and unclamped accuracy. In this context, system identification-based methods can play a vital role in determining and evaluating hidden relationships between the inputs (tool diameter, wall angle, sheet thickness, and step down) and two characteristics, namely, deformation energy and unclamped accuracy. The present work proposes comprehensive study based on the feedback-evolutionary system identification (FB-ESI) approach in predictive evaluation of multiresponse characteristics. The validation and robustness of the models were done based on statistical error metrics, cross-validation, new complexity metrics, and hypothesis tests. Furthermore, the model analysis based on the parametric and sensitivity procedures resulted in 2D and 3D plots that measure the nature of the two characteristics with respect to each of the four inputs. It was found that sheet thickness and wall angle influence the most the deformation energy and unclamped geometrical accuracy, respectively. The findings from this analysis are useful in monitoring deformation energy and thus promoting greener environment.