Abstract: The dual-stream functions method is improved and applied to establish the velocity field which strictly satisfies velocity boundary conditions of arbitrary caliber configurations. The rigid-plastic interface at the entrance is replaced by several planes so that the velocity discontinuity condition at the entrance is satisfied. Penalty function algorithm is applied to make the incompressibity condition be satisfied. Then, in complex caliber rolling, a general method for the simulation of three dimensional metal deformation is found and a general velocity field which can be used in arbitrary three dimensional metal flow is formulated.