The phenomenon of eccentric discharge is widely recognised as the most dangerous condition for thin-walled metal silos and the cause of many catastrophic buckling failures. A realistic pressure model for this condition appears in a regulating standard for the first time in EN 1991EN -4 (2006 on Actions on Silos and Tanks. However the structural consequences of its application are currently largely unknown. The behaviour of a silo subjected to these pressures is certainly very dependent on the aspect ratio of the silo, the granular solid properties and the discharge channel geometry.This paper explores the behaviour of four thin-walled cylindrical silos with stepwisevarying wall thickness and aspect ratios varying from intermediate to very slender, subject to the codified EN 1991-4 eccentric discharge pressures. It is shown that a silo design that was found to be very safe under the EN 1991-4 concentric discharge pressures becomes very unsafe under eccentric discharge. Further, as it is known that the aspect ratio has an important effect on the flow pattern in discharging granular solids, and that slender silos exhibit very different flow patterns from squat silos, it is currently not certain whether a suitable range of aspect ratio over which the codified eccentric discharge model is to be applied has been prescribed in the standard. This paper is the second of a pair. In the first, the behaviour of a set of example silos under the EN 1991-4 concentric discharge condition was studied. The same example silos are studied here under eccentric discharge.