Numerically controlled flame cutting machines used in shipyards are generally equipped only with line-segment and circle-arc moving capabilities. This paper attacks the problem of how to approximate a given curve of arbitrary shape by a sequence of line-segments and circle-arcs. The given curve is represented by the cubic spline interpolation curve formed by a set of net points on the curve. An efficient method based on the nature of cubic spline is then provided to approximate the interpolation curve by a sequence of linesegments and circle-arcs. This method has been practically employed by the China Shipbuilding Co. in production line. In order to save storage and expedite the approximation, an effective method is also provided for selecting a near minimal set of net points whose cubic spline interpolation curve can adequately represent the actual given curve. Although the techniques are developed for shipbuilding purpose, they can find applications in other fields.