Abstract: The transient response of an upper-convected Maxwell fluid flow in a circular tube is investigated by the method of Kantorvich and that of finite difference. With the help of the constitutive equation of the Maxwell fluid the equation of motion is reduced to a, partial differential equation of hyperbolic type. The solution of the problem by the variational method is in good agreement with the numerical results by the difference scheme. The results show that the variational method of Kantorovich is suitable ...