Dean instability of viscoelastic fluids obeying Giesekus model as their constitutive equation is investigated numerically in azimuthal, pressure-driven flow between two fixed, infinitely-long, rigid concentric cylinders at arbitrary gap spacing. Having determined the basic flow velocity profiles and stress fields numerically, the time evolution of small, axisymmetric perturbations superimposed on the basic flow was monitored using a normal-mode instability analysis. In an attempt to determine the onset conditions for the rise of secondary flow in the gap, terms non-linear in the perturbations quantities were dropped from the governing equations. To solve the eigenvalue problem so-obtained, use was made of the pseudospectral collocation method based on Chebyshev polynomials. The main objective of the work was to compute the critical Dean number (i.e., the Dean number at which stationary-mode, secondary flow start to appear in the gap) as a function of the Weissenberg number for different values of the mobility factor and gap spacing. Based on the results obtained in this work, one can conclude that at low to moderate Weissenberg numbers, fluid's elasticity stabilizes the Dean flow. Beyond a critical Weissenberg number, however, elasticity is predicted to have a destabilizing effect on the flow. The critical Weissenberg number decreases by an increase in the gap size, and also by an increase in the mobility factor. (C) 2012 Elsevier B.V. All rights reserved.