The objective of this study uses the plasticity theory of the slab method and the numerical analysis of the finite difference method to construct a mathematical model. And a computer program will be developed to evaluate the quality of the tubes formed by hydraulic expansion. Considering sticking and sliding modes, a mathematical model is proposed to predict the forming pressure needed to hydroform a circular tube into square and rectangular cross-sections and the thickness distribution of the product. In the sticking friction mode, it is assumed that the elements after contact with the die do not move or slide. Whereas, in the sliding friction mode, the element in contact with the die will continue to deform with the stress variation in the subsequent forming process. A series of FE simulations on tube expansion by a commercial FE code¡§DEFORM¡¨have been carried out. In addition, the experiment employing aluminum alloy AA 6063 that has been annealed to proceed the hydraulic expansion experiment. The comparisons between analysis and the result of forming pressure, corner radius and thickness distribution by experiment are verified the validity of this mathematical model. The effects of the forming parameters such as the die geometry, the material property of the tube, friction coefficient between the die and tube, etc., upon the expansion results, such as the forming pressure, corner radius, the tube contact distance with the die, thickness distribution after expansion, etc., are systematically discussed.