Abstract: The velocity field is devided into the basic and additional fields. The basic velocity field should satisfy given conditions on boundary, but the additional velocity field should only satisfy the uniform boundary conditions. Corresponding to those two parts of velocity field there are basic flow function and additional flow function. The basic flow function can be written definitly, while the additional flow function, according to the Weierstrass theorem, has been written as a family of vectors in complete space, i.e. a polynomial. With the aid of minimization of the total power the coefficients of the polynomial hare been defined. By using this method, the following results are obtained: velocity field, field of strain-rate, stress field, the back and front boundaries of plastic zone, the position of neuture point on the contact arc, and the rolling pressure acting on the contact surface of the strip.