The extrusion of section from round billet poses a great challenge for theoretical modeling of the process using upper bound method. The greatest difficulty in three-dimensional upper bound method is to determine kinematically admissible velocity field. The SERR (Spatial Elementary Rigid Region) technique is fairly applicable for analyzing extrusion of sections having re-entrant corners. A modified version of SERR technique has been used for extrusion of octagon sections from round billet through a linearly converging die. The circular cross section of the round billet is approximated by a regular polygon of equal area. The extrusion pressure has been computed for different boundary condition at the die billet interface. The optimum die geometry has been determined.