Plane strain bending (e.g. bending about a straight line) is a major sheet forming operation and it is practiced as brake bending (air bending, U-die, V-die and wiping-die bending). Precise prediction of springback is the key to the design of the bending dies and to the control of the process and press brake to obtain close tolerances in bent parts. In this paper, reliable mathematical models for press brake bending are presented. These models can predict springback, bendability, strain and stress distributions, and the maximum loads on the punch and die. The elasto-plastic bending model incorporates the true (nonlinear) strain distribution across the sheet thickness, Swift's strain hardening law, Hill's 1979 nonquadratic yield criterion for normal anisotropic materials, and plane strain deformation mode. The formulations and procedure have been programmed to simulate air bending and die bending process with U-die, V-die, and wiping-die, and simulation results compare well with experimental data. Air bending simulations show that the springback angle is proportional to the bending moment and the bent arc length between the punch and die. The bending moment and springback increase with strength, strain hardening, and normal anisotropy. Decreasing the bend arc length by reducing the die opening or die clearance is an effective way to reduce the springback. In air bending, springback can be compensated by overbending through a deeper punch stroke. The necessary ram stroke can be preset in the press controller using the predicted curve of springback vs. stroke. Based on the proposed model for springback, a number of new techniques to reduce springback are discussed, and an optimal bending die design with tractrix profile is suggested to reduce the sensitivity of the bending angle to the variations in press setup and stroke and to control the springback and tolerance in bent parts.