In this paper the unsteady Poiseuille flow of fractional Oldroyd-B viscoelastics fluid between two parallel plates is studied, which sheds light on the investigation on fractional differential equations. Stehfest algorithm for numerical inversion of Laplace transform is used for obtaining the numerical solutions, and its validity is verified by comparing the results with approximate analytic solutions. Then the laminar Poiseuille flow of fractional Oldroyd-B viscoelastic fluid is investigated by the Stehfest algorithm. Phenomena of velocity and stress overshootings are found, which are proved to be dependent on the order of fractional derivative. Simultaneously, compared with the integer constitutive equations, the fractional constitutive equations have wider scope of application. This conclusion was drawn based on the obvious fact that the integer constitutive equations are only special cases of the fractional constitutive equations.