In this note the velocity field and the associated tangential stress corresponding to the rotational flow of
a generalized Maxwell fluid within an infinite circular cylinder are determined by means of the Laplace and Hankel transforms.
At time
the fluid is at rest and the motion is produced by the rotation of the cylinder around its axis.
The solutions that have been obtained are presented under integral and series forms in terms of the
generalized G-functions. The similar solutions for ordinary Maxwell fluid, performing the same motion, are obtained
as particular cases of our solutions for
.