In recent years, one of the challenges in sheet metal forming was production of double curvature surfaces without mechanical tools and external forces. Forming with a heat source is a capable method for forming arbitrary 3D shapes with double curvature surfaces. However forming of even 2D shapes with a heat source is a very complicated thermo-mechanical process. Production of 3D shapes with a heat source is more complicated than 2D shapes. For this reason few researches in the field of forming of 3D shapes with a heat source have been reported. The aim of this thesis is investigating and proposing new methods for forming of double curvature surfaces with a heat source. In order to obtain a better knowledge in this field, in the first part of the thesis, we focused on the forming of 2D shapes with a laser heat source. These researches were focused on laser bending of tailor machined blanks. Laser bending of tailor machined blanks is more complicated than monolithic plates due to different thicknesses in these blanks. As a result of these studies a new irradiating scheme was proposed for laser bending of tailor machined blanks. Experimental and numerical results showed that the proposed irradiating scheme was a suitable method for laser bending of tailor machined blanks. Also, the effects of various process parameters such as irradiating method, laser power, beam diameter, number of scan passes and start point of scan path on the bending angle of tailor machined blanks were investigated based of statistical analyses. After this section, in the second part of the thesis our researches were focused on the production of double curvature surfaces with a heat source. For this purpose, forming of a bowl shaped surface with a spiral irradiating scheme and also production of dome and saddle shapes in two separate stages were investigated. Bowl shaped surfaces were formed from circular plates with spiral irradiating scheme and using flame as the heat source. Experimental and numerical results show that a bowl shaped surface with considerable amount of curvature can be successfully made by spiral irradiating scheme. Effects of spiral pitch, number of spiral passes and also in-to-out and reversely out-to-in spiral path on the obtained bowl shaped surface were investigated. Dome and saddle shapes were also investigated in two stages. Firstly with an analytical method a suitable irradiating scheme was proposed for forming of double curvature dome and saddle shapes. Then, performance of proposed irradiating scheme was investigated with experimental tests and numerical simulations. In the proposed method, first and second curvatures were sequentially produced in two subsequent steps. The results showed that the proposed irradiating scheme can be successfully used to make dome and saddle shapes with large deformations and reasonable symmetries. Using irradiating scheme proposed in this section, second curvatures of dome and saddle shapes were successfully formed from plates with various initial curvatures. Therefore, it was proved that the proposed irradiating scheme can be used to produce second curvatures of any desired shape from plates with any initial curvatures. Also, the effects of various process parameters on the second curvature of dome surface were investigated based on statistical analysis. Finally, a systematic method was proposed for producing dome shapes with arbitrary first and second curvatures. Keywords: Forming with a heat source, Tailor machined blanks, Double curvature plates, Dome shape surface, Saddle shape surface