A new upper bound method for the analysis of three-dimensional deformation in the at rolling of bars is proposed. In the conventional upper bound method, stress distribution is not calculated. Hence, a new method of calculating stress distribution is proposed in which the hydrostatic stress in each element and the contact stress on the contact surface between material and roll in each element are calculated. In the conventional upper bound method, the structure of the computer program also depends highly on the kinematically admissible velocity ΓΏelds assumed. Hence, a new method of analysis in which the structure of the computer program depends minimally on the kinematically admissible velocity ΓΏelds assumed is proposed. In the analysis of strip rolling, the calculated roll force and roll torque agree with the roll force and roll torque calculated from Sims' slab method. In the analysis of the at rolling of bars, the calculated width spread agrees with the width spread obtained by experiments reported in the literature. The e ects of a reduction in thickness, roll radius, material width-to-height ratio, front tension, back tension, and front and back tensions on the width spread, forward slip, roll force and roll torque are demonstrated. Hence, the validity of the new upper bound method is conΓΏrmed.