The ultimate goal of the metal forming industry is to form components made of a specific material into a required shape without experiencing wrinkling and spring back. Of the aforementioned difficulties, attention in This thesis is devoted to spring back resulting from unloading following stretch forming, hi spite of the exhaustive application of the process to form many engineering components, the design and selection of sheet materials and tooling geometry to minimize spring back still rely on the elusive trial and error approach. It is thus the objective of this thesis to avoid the adhoc approach by analyzing the process using the finite element method. Stretch forming of sheet metal is an important manufacturing process employed in several industries to form panels of complex and varied curvatures. The objective of this thesis to carry out a systematic study of stretch forming using the finite element method. Three aspects of the current problem are accordingly investigated. The first is concerned with the development of a finite element model of the stretch forming process using ABAQOUS software. The elastoplastic behavior of the blank materials is investigated using isotropic constitutive models. Imposition of frictional contact constraints at the tooling-sheet interface is also introduced using contact elements. The second aspect of the work is concerned with the spring back experienced by the deformed sheet following the punch release stroke. Several numerical techniques are introduced to define and quantify spring back. For this purpose, use was made of MATLAB software to allow the determination of spring back using four different accepted definitions. In the third, attention was focused to the validation of the finite element models. The Limiting Dome Height (LDH) benchmark test was also utilized as a verification tool. And the second alternative way is experimental result. The results obtained from these tests reveal close agreement with the finite element predictions of the deformed sheet spring back and load deflection curves. In case our study concerning the stretch forming for a un-symmetrical U shape piece that can use in air craft industries.In our study, we examine the effect of the mechanical properties, the geometry and interface parameters upon the resulting spring back. Key Words Stretch forming, Springback, Finite element, Un-symmetrical U piece.