A method and apparatus for bending flat thermoplastic laminates into structural shapes such as angles, channels, Z sections, J sections and I sections. In order to bend the laminate into the desired shape by appropriate tooling, heat is applied in a localized manner only to the area that is to be bent. The application of heat is sufficient to heat the laminate to its softening temperature in the bend area, and the plies of the laminate can thus slip in the bend area only as bending force is applied so that the bend can be made without the need to heat the entire laminate to the softening temperature.