This thesis is concerned with the design of press tool run-ofts. Run-off is the area on the punch surrounding the panel and its shape is of great importance to the control of metal flow during the draw. The design, although influenced by engineering considerations, is principally a geometric problem, which traditionally has been time-consuming. The overall objective is to reduce the run-oft definition time and hence improve the lead time. Current Austin Rover design procedures are described in Chapter 2 and form the basis of the C.A.D. program outlined in Chapter 3. This specification distils the need for a number of geometric algorithms. In general, obtaining the required continuity between the panel and run-off surface will require some degree of boundary curve approximation. Chapter 4 details four alternative approximation techniques which are compared in Chapter 5; and constitute the main results of the thesis. The salient issues of run-off surface interpolation are considered in Chapter 6.