The velocity field and the shear stress corresponding to the unsteady flow of a generalized Oldroyd-B fluid in an infinite circular cylin-der subject to a longitudinal time-dependent shear stress are determined by means of Hankel and Laplace transforms. The exact solutions, writ-ten in terms of the generalized G-functions, satisfy all imposed initial and boundary conditions. The similar solutions for ordinary Oldroyd-B, ordi-nary and generalized Maxwell, ordinary and generalized second grade as well as for Newtonian fluids are obtained as limiting cases of our general solutions.