The paper presents a novel solution for improving the accuracy of the wall area of parts manufactured by single point incremental forming. Thus, a forming tool with a special design that works according to the principle of circumferential hammering is deployed, with a direct improving effect of the forming conditions and consequently of the dimensional accuracy of the part. The research is focused on an experimental study of frustum-of-cone shapes manufactured from sheet metal blanks of DC05 deep drawing steel of 1 mm thickness. A typical customary technological setup is used for the single point incremental forming process, without any additional elements, and two forming tools, a hemispherical and a special one, which use the circumferential hammering effect. Several preliminary tests using both tools were performed in order to prove that part accuracy can be significantly improved by using the circumferential hammering tool. The research was further expanded to investigate the influence on part wall dimensional accuracy of three factors: tool spindle speed, tool feed rate and part dimensional configuration. Using a full factorial plan of experiments the results of 32 test runs were processed. All parts were machined adequately, free of any material fracturing. Based on the achieved machining accuracy of the part walls, precision mathematical models were developed for the prediction of part dimensional accuracy in those areas. The mathematical models were validated by practice, as the predicted accuracies were matched by the experimental results.