In this paper, the unsteady lineal flows of a second grade fluid and of a Maxwell one, between parallel plates, are investigated. The velocity fields corresponding to the flow induced by a constantly accelerating plate as well as those for the flow caused by the impulsive motion of the plate are determined. The solutions that have been obtained satisfy the associate partial differential equations and all imposed initial and boundary conditions. They also reduce to those for Newtonian fluids as limiting cases. Finally, some conclusions and illustrative comparisons are also presented.