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The most serious loading condition for slender thin-walled metal silos has long been recognized to be the condition of discharge, with eccentric discharge causing more catastrophic failures than any other. Two key reasons for this high failure rate are the difficulties in characterizing the pressure distribution caused by eccentric solids flow, and in understanding the associated unsymmetrical stresses in the silo wall. Few studies have addressed either the linear elastic behavior of such a silo or its buckling failure under eccentric discharge. In this study, the eccentric discharge pressures are characterized using the new rules of the European Standard EN 1991-4 on Silos and Tanks. This novel description of unsymmetrical pressures permits a study of the structural behavior leading to buckling during eccentric discharge, including the critical effects of change of geometry and imperfection sensitivity, to be undertaken using geometrically and materially nonlinear computational analyses. The mechanics of the behavior are found to be quite complicated. A silo which is safe under axisymmetric loading is found to be susceptible to catastrophic stability failure under eccentric discharge. DOI: 10.1061/(ASCE)EM.1943-7889.0000112 CE Database subject headings: Thin shell structures; Solids flow; Silos; Structural stability; Buckling; Nonlinear analysis; Computer analysis. Author keywords: Thin shell structures; Solids flow; Silos; Structural stability; Buckling; Nonlinear analysis; Computer analysis.