Single-point incremental forming (SPIF) process is an emerging sheet metal forming process in which constraint of using dedicated press tools is eliminated. Some process limitations like poor surface finish, longer forming time, higher geometrical error, and uneven wall thickness distribution restrict its applicability in sheet metal industry. But SPIF process with dummy sheet has the capability to overcome some of the prevailing limitations of SPIF process. In the present paper, influence of dummy sheet thickness, step size, wall angle, and feed rate on geometrical error in terms of root-mean-squared error (RMSE) of formed part is investigated. Box Behnken design is used to design the experiments. From the analysis of experimental result, it is found that dummy sheet thickness, step size, and wall angle are significant process parameters influencing RMSE. No significant influence of feed rate on RMSE is observed. RMSE increases with increase in dummy sheet thickness and wall angle, while it decreases with increases in step size. As feed rate increases, there is nominal decrease in RMSE which is desirable. So higher feed rate is recommended to reduce forming time. Further, empirical model is developed to predict RMSE. Also, optimization of process parameters is performed to minimize RMSE. Confirmation experiments were performed in order to check the accuracy of developed predictive model and it is found that predicted results are in good agreement with experimental results. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd 2021.