In this paper, we have studied the rotational flow of a generalized second grade fluid between two infinite coaxial circular cylinders. The velocity field and the shear stress obtained by means of Laplace and Hankel transforms are presented under series form in terms of generalized functions. At time t = 0, the fluid and cylinders are at rest. At t = 0⁺, both cylinders suddenly begin to rotate, about their common axis, with a constant angular acceleration. The obtained solutions can be specialized to give the similar solutions for ordinary second grade and Newtonian fluids performing the same motion.