The simple position-dependent whirling mechanism proposed by Blevins for single across-stream tube rows is extended to model the effects of mechanical coupling between tubes and whirling in two dimensional tube banks. The model is in reasonable agreement with experiment for staggered arrays but not for in-line arrays. A wake galloping model is suggested for in-line arrays which is capable of producing agreement with experiment. The use of the Pettigrew design criteria for tube banks is also critically assessed. It is suggested that the use of a fixed "whirling" constant K for all structural mode shapes of a tube array may be too restrictive for low frequency, long wavelength modes, whereas a "whirling" constant dependent on tube array mode shape is more useful for design purposes. A discussion has been included of the relevance to real heat exchangers of flow tests on uncoupled tube arrays and the effects of detuning tubes in such arrays.