This paper depends on a new analytical method to calculate relative deformation energies for complex die shape by using upper bound theory which is an important method to solve technical problem in the field of metal deformation .This study divides the complex shape to a number of sectors for counting the deformation energies and then to find the total energy requirement for extrusion process in die with arbitrary linear function. This study uses (H) section which represents one of complex shapes to calculate the relative deformation energies for it, taking into account the effects of friction factor , relative die length and reduction of area . The results of the present study are compared with M.KIUCHI study and found it in a very good agreement
