In this paper, the upper bound method has been used in analysis of the flat rolling process and prediction of internal defects for a strain-hardening material. The arc of contact has been replaced by a chord. The inlet shear boundary of the deformation zone has been assumed as an exponential curve and the boundary at the exit has been assumed as a cylindrical surface. A kinematically admissible velocity field has been proposed and internal, shear and frictional power terms have been derived. By minimizing the total power with respect to the neutral point position and the shape of the inlet shear boundary, the rolling torque has been determined. A criterion has been presented to predict the occurrence of the internal defects for given rolling conditions. Comparison of the analytically developed approach for rolling torque and internal defects with published theoretical and experimental data shows generally good agreement.