A Floquet linear stability analysis has been performed on a viscoelastic cylinder wake. The FENE-P model is used to represent the non-Newtonian fluid, and the analysis is done using a modified version of an existing nonlinear code to compute the linearized initial value problem governing the growth of small perturbations in the wake. By measuring instability growth rates over a wide range of disturbance span-wise wavenumbers alpha, the effects of viscoelasticity were identified and compared directly to Newtonian results. At a Reynolds number of 300, two unstable bands exist over the range 0 <= alpha <= 10 for Newtonian flow. For the low alpha band, associated with the "mode A" wake instability, a monotonic reduction in growth rates is found for increasing polymer extensibility L. For the high a band, associated with the "mode B" instability, first a rise, then a significant decrease to a stable state is found for the instability growth rates as L is increased from L=10 to L=30. The mechanism behind this stabilization of both mode A and mode B instabilities is due to the change of the base flow, rather than a direct effect of viscoelasticity on the perturbation. (C) 2011 Elsevier B.V. All rights reserved.