A review of all known theoretical models of fluidelastic instability for cylinder arrays subject to fluid cross-flow is presented. Particular emphasis is given to the physics of the different instability mechanisms, and the assumptions made are analysed and discussed. Comparison are made between the models, and with available experimental data; these comparisons are in terms of the critical flow velocity for instability to occur and of the subcritical response of cylinders in the arrays. Despite the considerable differences in the theoretical models, there is some agreement in the general conclusion obtained. In particular, it is shown that the most important parameter for predicting fluidelastic instability is the unsteady nature of the interstitial flow in the array; specifically, the phase-lag between cylinder motion and fluid forces generated thereby. Methods appropriate for using the analyses, which are predominantly two-dimensional in nature, to predict the stability of three-dimensional heat exchanger spans subject to nonuniform flow are also evaluated. Finally, the effect of nonlinearities, both structural and fluid, on the post-instability behavior is reviewed. For loosely supported tubes with impacting occurring at the loose supports, the possibility of chaotic motion, with a consequent increase in wear rate, is predicted.