When constructing a rigid tool surface with fillets using triangular Bézier surface patches for an FE forming simulation, it is difficult to determine the number of segments required to accurately model a blend arc. This paper presents a combined numerical and analytical method to investigate the error of approximating circular arcs using cubic Bézier curve segments. It is established that there is a linear variation of the error with respect to the Tangent Magnitude Parameter (TMP) in certain regions, and an approximate linear variation of the error against the number of curve segments in log–log scales. In addition, the location of the maximum error and its variation with respect to the TMP are illustrated and analysed. The results obtained are applied to the creation of rigid tool surfaces for FE forming simulations. Two FE analyses are carried out: one to simulate the process of superplastically forming a 3D rectangular box with fillet surfaces, and the other to wrap a decorative pattern onto an axisymmetric ceramic pot.